Nah, this thing with the planet moving under you is stupid because it assumes a fixed reference frame which is not a thing in our universe. Any movement is always relative to something. You can't just "stay in place". Having the Earth move from under you is very arbitrary.
There's a ton of issues with time travel. That could be one, but most fictional time-travel devices can be said to accommodate for the difference in distance. It would just be boring to explain on-screen.
That's why doctor who works, its very clear about the fact that TARDIS travels in spacetime, it can do only time, only space or both space and time and they can get away with time traveling and still staying on earth