So... when someone shows up in this timeline... does that mean they weren't here before? Like... everyone I see on a regular basis is still around. What if one of them pops over from the other timeline suddenly? Why aren't there then two of them? And if they are still in the old timeline, is that a new version of them? Or did that version of them split into two and one ended up here, and the one that was already here fizzled out of existence?
Every time I think about writing a time travel story I end up doing this and decide it's not worth the effort.