This has never been consistent. In "The Five Doctors" the First and Second Doctors remember the events of the Three Doctors. In "Time Crash" the Tenth Doctor remembers what happens from the Fifth Doctor's perspective.
However, at the start of the Three Doctors, "The Five Doctors" and the Two Doctors, the later Doctors have no memory of the events that they are about to experience. In "The Day of the Doctor" the Eleventh Doctor remembers that he is about to meet the earlier Doctors, but has no memory of what he is actually going to experience. The explanation is that the timestreams were out, so every Doctor except the most recent will forget the events. However, in "The Five Doctors" the explanation is that Rassilon wiped the memories of all but the most recent Doctor. And of course in "Time Crash" the Doctor did remember it.