I've been involved in discussions of RL time-travel, recently, and on forums not primarily DF-facing, so I won't go into that. But for a game-perspective.
Time travel back to a prior (possibly specially 'placemarked', with accompanying save-data issues) point of time could be treated as "New Branch of causality, future not necessarily determined by passage of old branch". Some things (characters accompanying a wagon) could be the same if no on-screen or off-screen events act differently in the various randomness/player-interaction levels. Obviously if one's "one back in time" character killed one of them, then it would be different.
As for self-on-self interactions, maybe the Handwavium-powered time machine/magical device can only send matter back to where that matter was originally (give or take), overlaying experience and (soon to be invalidated) memories upon the person's original body, so that in the new branch there is still the same character, but with knowledge (and body mass/scars) strength. The 'original' character still resides in the original branch, leading up to the point of return, but is inaccessible to this older character's experience. It's all different. You can't wander around and then meet up with the previous branch's character at the place he built his castle.
Travel back beyond the lifetime of the character may either be not allowed or would produce one (from 'nothing') fully capable of killing any number of identifiable ancestors without phasing out his or her own existence, as he/she is born of the original (now not going to happen) timeline, not of the one he or she is helping to form afresh, within which there may or may not be a person that is their younger self. And if that younger self does arise, then they're a game-controlled 'zombie', and need not (the excuse being that traveler-self has changed the environmental influences?) follow anything like the same path in life as the traveler followed to reach the point of departure.
This is not how I see 'RL' time travel happening (I have this "static tapestry of time" idea in mind, which requires a meta-existence and entire-history overview to ensure this is stable), and is more of a standard lazy-style fictional fudge than anything fully consistent, but it would be a viable solution for game stability with a time-travel option. IYSWIM