Salam. I myself have noticed this hadith in many places which even say that it is Ahsan Hadith. I am going to tell you a basic principle of Islam which is:
You won't be asked about your deeds which you didn't know about. But once you understood that it is prohibited in Islam and then you continued performing that bad deed, you will be asked and will be responsible for that.
As almost many of companions did bad deeds before they came into Islam and they wont be asked about them. Same is the case for us but we should repent on those.
Now some references from Quran and Hadith.
Allah says in the Holy Quran Chapter 3 Surah Ale Imraan verse 135-136:
Allah likes such good people very much, who, if ever they commit a base deed or wrong their own soul by the commission of a sin, remember Allah instantly, and ask for forgiveness from Him for their shortcomings. For who, but Allah, can forgive sins? (And Allah loves those) who do not knowingly persist in the wrongs they did. These will be rewarded with forgiveness from Allah, and with Gardens beneath which canals flow, and they will reside therein forever! How excellent is the reward of those who do good deeds!
Allah says in the Holy Quran Chapter 6 Surah Anaam verse 54:
When those come to you who believe in Our Signs, say: "Peace be on you! Your Lord had inscribed for Himself (the rule of) Mercy. Verily if any of you did evil in ignorance, and thereafter repented and amended (his conduct), Lo! He is Oft-Forgiving, Most Merciful."
Sahih Muslim Book 1, 0218:
It is narrated on the authority of Abdullah b. Mas'ud: We once said: Messenger of Allah, would we be held responsible for our deeds committed in the state of ignorance? He (the Holy Prophet) observed: He who did good deeds in Islam would not be held responsible for what he did in the state of ignorance, but he who committed evil (after having come within the fold of Islam) would be held responsible for his previous and later deeds.
Sahih Muslim Book 1, 0217:
It is narrated on the authority of Abdullah b. Mas'ud that some people said to the Messenger of Allah (may peace be upon him): Messenger of Allah, would we be held responsible for our deeds committed in the state of ignorance (before embracing Islam)? Upon his he (the Holy Prophet) remarked: He who amongst you performed good deeds in Islam , He would not be held responsible for them (misdeeds which he committed in ignorance) and he who committed evil (even after embracing Islam) would be held responsible or his misdeeds that he committed in the state of ignorance as well as in that of Islam.
So My Brother, the salaat when you didn't know are not obligatory to be prayed again but the salaat when you will pray in future and do this mistake then according to Hadith and some stories of companions should be prayed again. And never forget to seek forgiveness for those mistakes!! I hope I could do a little to help you....