Are there reports mentioning this in tafsir books?
Yes many reports in most early tafsir books seem to come to the conclusion and the consensus that the story mentioned in surat Yasseen يس in the verses (13-29) is referring to the city Antakya أنطاكية (Antioch) and that the three messengers were sent by 'Isa ().
Imam al-Qurtubi even mentioned that there's consensus about the location in his tafsir saying:
هذه القرية هي أنطاكية في قول جميع المفسرين فيما ذكر الماوردي . (Source Tafsir al-Qurtubi in Arabic)
This city is Antioch in the opinion of all scholars of tafsir as was mentioned by al-Maawardy
Some of these reports have been compiled by ibn Kathir in his tafsir of verse 14:
When We sent to them two but they denied them, so We strengthened them with a third, and they said, "Indeed, we are messengers to you."
Where the reports also named the city and the messengers:
In the reports that he transmitted from ibn 'Abbas, Ka'ab al-Ahbar and Wahb ibn Munabbih - Ibn Ishaq reported that it was the city of Antioch, in which there was a king called Antiochus the son of Antiochus the son of Antiochus, who used to worship idols.
Allah sent to him three Messengers, whose names were Sadiq, Saduq and Shalum, and he disbelieved in them.
It was also narrated from Buraydah bin Al-Husayb, 'Ikrimah, Qatadah and Az-Zuhri that it was Antioch. (Source Tafsir ibn Kathir)
Nevertheless ibn Kathir pointed out that:
Some of the Imams were not sure that it was Antioch, as we shall see below after telling the rest of the story, if Allah wills.
Before going on with his reports and explanation (Same source with some additional inline comments):
(When We sent to them two Messengers, they denied them both;)
means, they hastened to disbelieve in them.
(so We reinforced them with a third,)
means, "We supported and strengthened them with a third Messenger".
Ibn Jurayj narrated from Wahb bin Sulayman, from Shu'ayb Al-Jaba'i, "The names of the first two Messengers were Sham'un (Simon?)and Yuhanna (John?), and the name of the third was Bulus(Paulus, Paul?), and the city was Antioch (Antakiyah).
(and they said)
means, to the people of that city,
(Verily, we have been sent to you as Messengers.)
meaning, "from your Lord Who created you and Who commands you to worship Him Alone with no partners or associates". This was the view of abu Al-'Aliyah. Qatadah bin Di'amah claimed that they were messengers of the Messiah, peace be upon him, sent to the people of Antioch.
This view that this messengers were sent by 'Isa is also present in the tafsirs of scholars such as al-Baghawi, al-Kashaf (az-Zamakhshari), a-Shawkani, al-Naydawi, ibn Jazy and ar-Razi. But the reports which ibn Jarir at-Tabari mainly first complied have a disconnected narrator chain.
Note that ibn Kathir lived between 701 a.H. and 774 a.H. due to his mentioning of his sheikh al-Mizzi in his tafssir of surat al-Anbiyya' -asking Allah to give him a long life- this tafssir was already in work 742 a.H. and as his mate az-Zayla'iy الزيلعي was referring to it it was already finished by 762 a.H.. The corresponding wikipedia Article in Arabic claims it was finished 759 a.H.
While al-Qurtubi died 671 a.H..
The second view saying that the messengers were sent by Allah not by 'Isa () is also presented by ibn Jarir at-Tabari and al-Qurtubi too. While al-Qurtubi only mentioned it ibn Jarir added a few supporting reports (see here in Arabic).
What is the truth of this claims
As said earlier many early tafsir books mentioned the reports above and hardly pointed at an issue as Allah said in the verse mentioned above:
When We sent to them ...
Which actually doesn't confirm the claim that 'Isa sent 2 messengers to a city, but Allah did.
This also becomes clear from the answer of the disbelievers who said in (36:16):
..."You are not but human beings like us, and the Most Merciful has not revealed a thing. You are only telling lies."
Only disbelievers expect a miraculous creator or angel to be sent as a messenger from Allah as the qur'an show in other verses. They wouldn't exclaim this in case a human has sent humans to them!
A further issue is that the verse (36:29):
It was not but one shout, and immediately they were extinguished.
In this interpretation would against:
And We gave Moses the Scripture, after We had destroyed the former generations, as enlightenment for the people and guidance and mercy that they might be reminded. (28:43)
Which ibn Kathir commented:
(after We had destroyed the generations of old)
After the revelation of the Tawrah, no nation would again be punished with an overwhelming calamity; instead the believers were now commanded to fight the enemies of Allah among the idolators, as Allah says:
(And Fir'awn, and those before him, and the cities overthrown committed sin. And they disobeyed their Lord's Messenger, so He seized them with a strong punishment) (69:9-10). (Source Tafsir ibn Kathir)
Based on a report which was reported by ibn Jarir at-Tabari and abi Hathim on the authority of abu Sa'id al-Khudri and which ibn Kathir actually quoted -both- in his tafsir (See here in Arabic). This reports say that the punishment mentioned in this verse was the last one Allah () ordered or made, as afterwards He () ordered the believers to fight disbelievers.
And finally the history of Antioch and how it became christian doesn't claim that there was any punishment by Allah.
This was mentioned in the end of this story where ibn Kathir displayed and held a view which ibn Taymiyyah adapted from abu al-'Aliyyah. I'll display here the tafsir starting with the exegesis of verse (36:29):
(It was but one Sayhah and lo! they (all) were still.)
He said, "So Allah destroyed that tyrant king, and destroyed the people of Antioch, and they disappeared from the face of the earth, leaving no trace behind. It was said that the words
(And We sent not against his people after him an army from the heaven,)
mean, another Message to them. This was the view of Mujahid and Qatadah. Qatadah said, "Allah did not rebuke his people after they killed him,"
(It was but one Sayhah and lo! they (all) were still).
Ibn Jarir said, "The former view is more correct, because the Message does not need to be brought by an army." The scholars of Tafsir said, "Allah sent Jibril, peace be upon him, to them, and he seized the pillars at the gate of their city, then he hurled one Sayhah upon them and lo! they (all) were still, to the last man among them, and no soul was left in any body."
After this ibn Kathir shows the flaws in the view of earlier scholars who interpreted the city to be Antioch and the sender of the messengers to be 'Isa () in three points:
We have already referred to the reports from many of the Salaf that this city was Antioch, and that these three Messengers were messengers sent from the Messiah 'Isa bin Maryam, peace be upon him, as Qatadah and others stated. This is not mentioned by any of the later scholars of Tafsir besides him, and this issue must be examined from a number of angles. (The first) is that if we take this story at face value, it indicates that these men were Messengers from Allah, may He be glorified, not from the Messiah, peace be upon him, as Allah says:
(It was but one Sayhah and lo! they (all) were still)." Ibn Jarir said, "The former view is more correct, because the Message does not need to be brought by an army." The scholars of Tafsir said, "Allah sent Jibril, peace be upon him, to them, and he seized the pillars at the gate of their city, then he hurled one Sayhah upon them and lo! they (all) were still, to the last man among them, and no soul was left in any body." We have already referred to the reports from many of the Salaf that this city was Antioch, and that these three Messengers were messengers sent from the Messiah 'Isa bin Maryam, peace be upon him, as Qatadah and others stated. This is not mentioned by any of the later scholars of Tafsir besides him, and this issue must be examined from a number of angles.
The first is that if we take this story at face value, it indicates that these men were Messengers from Allah, may He be glorified, not from the Messiah, peace be upon him, as Allah says:
(When We sent to them two Messengers, they denied them both; so We reinforced them with a third, and they said: "Verily, we have been sent to you as Messengers.")
("Our Lord knows that we have been sent as Messengers to you. And our duty is only to convey plainly (the Message).")
If they had been from among the Disciples, they would have said something to indicate that they had come from the Messiah, peace be upon him. And Allah knows best. Moreover, if they had been messengers sent by the Messiah, why would the people have said to them,
("You are only human beings like ourselves")
The second is that the people of Antioch did believe in the messengers sent by the Messiah to them. Antioch was the first city to believe in the Messiah, and it is one of the four cities in which there are Christian patriarchs. These cities are: Jerusalem, because it is the city of the Messiah; Antioch, because it was the first city where all of the people believed in the Messiah; Alexandria, because it was in that city that they agreed to reform the hierarchy of patriarchs, metropolitans (archbishops), bishops, priests, deacons and monks; and Rome, because it is the city of the Emperor Constantine who supported and helped to establish their religion. When he adopted Constantinople as his city, the Patriarch of Rome moved there, as has been mentioned by several historian, such as Sa'id bin Batriq and others, both People of the Book and Muslims. If we accept that, then the people of Antioch were the first to believe, but Allah tells us that the people of this town rejected His Messengers and that He destroyed them with one Sayhah and lo! they (all) were still. And Allah knows best.
The third is that the story of Antioch and the Disciples of the Messiah happened after the Tawrah had been revealed. Abu Sa'id Al-Khudri, may Allah be pleased with him, and others among the Salaf stated that after revealing the Tawrah, Allah, may He be blessed and exalted, did not destroy an entire nation by sending a punishment upon them. Rather, He commanded the believers to fight the idolators. They mentioned this when discussing the Ayah:
(And indeed We gave Musa -- after We had destroyed the generations of old -- the Scripture) (28:43).
This implies that the city mentioned in the Qur'an is a city other than Antioch, as also stated by more than one of the Salaf. Or, if we wish to keep the same name, it is possible that it is another Antioch, not the one which is well-known, for it is not known that it (the famous Antioch) was destroyed, either during Christian times or before. And Allah knows best.
From the above we may safely say that ibn Kathir quoted these reports and refuted them at the end of the story so who ever shares this information without quoting ibn Kathir's real position on the topic is falsely quoting ibn Kathir.
Nevertheless one could also say that there's a difference of opinion among scholars on this topic.
See also fata islamqa #170943 in Arabic.