It is not possible to know who is being quoted without knowing the actual stories.
The first story you heard about a person who committed all the sins in his entire life comes from a hadith mutawātir:
عَنْ أَبِي سَعِيدٍ ـ رضى الله عنه ـ عَنِ النَّبِيِّ صلى الله عليه وسلم: أَنَّ رَجُلاً كَانَ قَبْلَكُمْ رَغَسَهُ اللَّهُ مَالاً فَقَالَ لِبَنِيهِ لَمَّا حُضِرَ أَىَّ أَبٍ كُنْتُ لَكُمْ قَالُوا خَيْرَ أَبٍ. قَالَ فَإِنِّي لَمْ أَعْمَلْ خَيْرًا قَطُّ، فَإِذَا مُتُّ فَأَحْرِقُونِي ثُمَّ اسْحَقُونِي ثُمَّ ذَرُّونِي فِي يَوْمٍ عَاصِفٍ. فَفَعَلُوا، فَجَمَعَهُ اللَّهُ عَزَّ وَجَلَّ، فَقَالَ مَا حَمَلَكَ قَالَ مَخَافَتُكَ. فَتَلَقَّاهُ بِرَحْمَتِهِ
Narrated Abu Sa'id: The Prophet (ﷺ) said, "Amongst the people preceding your age, there was a man whom Allah had given a lot of money. While he was in his death-bed, he called his sons and said, 'What type of father have I been to you? They replied, 'You have been a good father.' He said, 'I have never done a single good deed; so when I die, burn me, crush my body, and scatter the resulting ashes on a windy day.' His sons did accordingly, but Allah gathered his particles and asked (him), 'What made you do so?' He replied, "Fear of you.' So Allah bestowed His Mercy upon him (forgave him).
— Sahih al-Bukhariو Book 60, Hadith 145
This authentic hadith, in particular, does not have any mention of the person being in Jannah now, or that this is where he will end up in the hereafter after his account is established. Only Allah knows.
I have not found any reference to the second story.
In general, the final destination for all of us is indeed on the Day of Judgment, but this does not mean there is no reward or punishment before. There are numerous stories in the Qur'an of punishment taking place in this life, in the grave and in there hereafter.
It is to be noted, however, that a common instrument in the Arabic language is the use of the past tense about future events to indicate that the event in question is so close:
أَتَىٰ أَمْرُ اللَّهِ فَلَا تَسْتَعْجِلُوهُ سُبْحَانَهُ وَتَعَالَىٰ عَمَّا يُشْرِكُونَ
Allah's commandment has come, therefore do not desire to hasten it; glory be to Him, and highly exalted be He above what they associate (with Him).
— Surat An-Nahl 16:1
In this verse, Allah is telling us about a future event (the Hour) that it has already come upon us, and that we should not hasten it. We know the Hour has not yet arrived, but the use of the past tense is to indicate it is close. So one may hear stories referring to reward or punishment already taking place to indicate it is near, and not necessarily that it has taken place.
One final point, it is always advisable to check the reference of stories one hear to validate their authenticity.