Space and time are the same thing. Spacetime. Time travel would necessarily also by teleportation if you are traveling instantaneously through spacetime. Unless of course your travel is continuous like it is currently for all of us, just sped up, slowed down or reversed.

Also there is no objective point of reference for location in the universe, only relative points of reference. In other words, you are always some distance in some direction from some thing. But you never have objective stable coordinates relative to the universe itself. There is no "center" or other fixed point of the universe. So the earth is moving, yes, but only relative to other independent celestial bodies. And those bodies are moving, too, relative to other bodies. Their movement is always relative to a non-absolute frame of reference. No movement is objective to the universe, it's all relative.

So it would be illogical to expect the earth to have moved X miles away in Y direction if you teleported one second into the past/future because that would presuppose that your location was objective and absolute in the universe at the point of time traveling and the earth moved relative to your absolute location. It would break known physics if that were the case, as much as time travel itself would.