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
That’s exactly like being a bit closer to the bottom of a steep gravity well.
Yes, we could tell if they took a precise clock with them. In fact, we have to account for an even smaller discrepancy in order for GPS to work: we here stuck further down in Earth’s gravity well travel through time and extra ten milliseconds or so per year vs. an orbiting satellite.