While PBEMing, after I choose to save my turn, and before the Save file interface appears, the game shows me moves made by other tribes, including the tribe belonging to the other human player - who is in fact not yet playing his turn.
I have seen these units go so far as to capture another tribe's city. Curiosity got the best of me, so I replayed that turn a few times just to observe. So I observed those same units failing to capture the city

, capturing and then razing the city

, and forgoing to attack it at all

.
I asked my game partner about this, and he's never observed the phenomenon of the opposing human player's units moving before the save.
So I gather that I have switched on some option some where that he never switches on. I don't see the point of it, though. Try as it might, the AI cannot accurately predict what action the human player will actually take, and when the human player actually finishes his turn and passes it back to me, his units are
not in the locations where the AI showed them just before the file saved.