Kivult, this seems to be the case that some Tannai had their own private records, but it is clear tha they were incomplete. For example, a recent daf had it hat R Akiva knew about machloket between b’Shammai and b’ Hillel but did not remember who said what.
r Ashi is considered to be of generation that organized Bavli, butI think academics find several later generations continued editing.