I think the easiest way to visually represent the way time travel works (in my opinion) is with a piece of string. Feel free to follow along with this at home for a hands on visual.
Think of the string as someone's path through time. Stretch the string out so it forms a straight line. Mark the general beginning and end of this line. The string should always stay more or less parallel to this line. The straight line would be the timeline, with the beginning of the string representing the person's birth on the timeline, and the end their death.
When you get a place where they moved backwards in time, you would take the exact position they would have been on the string and cut it. You then take the newly cut piece and move it to where they went back to on the timeline. You now have two strings (still representing the same person) that overlap at a certain point on the timeline.
If they move forward, you do the same thing, only this time instead of overlap, you get a gap, where they weren't anywhere in the timeline.
So you end up with something like this:
2000 -Person A is born.
2005 -Person A turns 5 years old, on the same day a 45 year old Person A shows up from the future.
2010 -Person A turns 10, while the Person A from the future turns 55.
2045 -Person A grows up to be 45, and goes back in time to the year 2005. Person A from the future is now 90.
2050 -Person A dies at the age of 95.
There's some overlap, but ultimately this person only lived one lifetime, even if it was compressed into 50 years. I think getting into separate timelines and dimensions only serves to complicate things more than they need to be. Of course, they may need to be complicated in that way, but from what we currently know, I doubt it.
But I think I understand.
