Some ideas are:
- You branch off into another timeline and your actions make no difference to the previous timeline
- You’ve already taken said actions but just didn’t know about it so nothing changes
- Actions taken can have an effect (so you could suddenly erase yourself if you killed your parents)
- Only “nexus” or fixed events really matter, the timeline will sort itself out for minor changes
- something else entirely
I mean I would say causality would be followed. So you change things and essentially create a new timeline. The only thing with that is if your time travel system could handle it. If you go back will you go back to your old timeline or your new one? Maybe you could choose but not necessarily. and of course any time you return to a point before you left you are further creating a new timeline. You would have to return after you left to preserve whatever you return to. So basically causality follows the individual and timelines pretty much always get created when time travel happens. Another interesting possibility is if you can manage to not change anything at all maybe you could stay in the original timeline. Its hard to say if that could even happen though as it would need at some point an original timeline without time travel to work off of.