Yes, that is the first thing written in my notes that are pictured at the end of the post: "or perhaps going back in time requires remaining at the same point in space (so you'd probably end up in outer space)..."

However, that is a supposition that doesn't necessarily have mathematical or physical basis, I came to realize.

It's possible that time travel would transport you through only time and not space, yes. However, it seems to be more likely that it would transport you through spacetime. In a closed timelike curve, for example, you could go as far back as to when and where the time machine was created. I should've mentioned that in the post. Your travel would be restricted to the location of the time machine.

At least that would be the case with a CTC, which looks to be the most likely future form of time travel.

Excellent point, though!