Well, Herodotus is another case of weird ancient history. In his book the Histories he talks about his methodology, which was to travel around and collect history from people as they told it. As you can imagine his book is full of tales of monsters and gods and stuff like that.

Interestingly he does mention at times that he thinks certain stories are ridiculous, but then carefully mentions that he must remain consistent and that he is gathering histories as told by the locals. So a lot of times he will sort of cite sources by saying: "I heard this story in Egypt from the priests at the temple of Ted." Or something like that.

Some of the commentary I read about his works was that it was probably more reliable for what was recent history at the time. So if he says, "Last year the river flooded." That is probably pretty reliable, while if he says "A thousand years ago there was this massive fire that made popcorn." Less so.

According to Anthony A. Barrett in the introduction to Tacitus The Annals, ancient historians were more concerned about improving upon the work of their predecessors than paying particular attention to primary sources. They also generally didn't mention their sources by name, more often simply saying 'people' or 'certain writers' etc.

Tacitus himself mentions using some primary sources, such as the acta diurna (Daily Record) and directly mentions using the Senate records himself on one occasion. He also sometimes mentions in the text where his sources diverge and so shows how what one person says differs from another. Tacitus is also very interesting because we can check what he said against inscriptions found. For example, the Tabula Hebana gives a list of honours approved for the late Germanicus by the Senate. Tacitus gives quite a negative impression of Tiberius in his handling of the ceremonies; he and his mother were absent during the ceremonies to mark Germanicus' death and they put pressure on Germanicus' mother Antonia not to take part. However, the inscription shows Tiberius being very actively involved, delivering eulogies himself.

If I remember correctly, Thucydides, although stating how he will be objective and careful, never actually mentions any primary sources. Edit#: Also, Seutonius in his Lives of the Caesars actually uses some letters sent by various emperors (Augustus in particular I think) since he probably had access to these when working in the imperial court.