Dissociation can involve time distortions and memory problems though, so it could be something like that--not DID, but some sort of dissociative distortion of a specific nature.

Like, for instance (maybe, just one possibility) the man in hat dream might feel like a memory of an old dream but isn't. Could be a real past experience or a screen memory for a real experience, etc.

Weird stuff like this happens with alien abductees who don't know each other. I'm not saying I understand it, I'm just saying it happens there too.