The movie Primer offers an interesting solution to this common problem of time travel science-fiction — which is usually ignored otherwise.
In the film, the time machine is a container for a field, or volume, that is segregated from the rest of the universe. Objects can enter and exit the field at either end of its duration, the interval over which the machine is active. So, although you’re able to travel backward in time, it’s only to the moment when the machine was last turned on in the past, and the field was established. Also, it’ll take you a lousy one minute per minute to make the journey — so if you’re travelling back to a week ago last Tuesday, you’d better pack a really good lunch or two. And bring a sleeping bag.
Anyway, the “Earth moving out from under you” problem is solved, fictionally, by having the time traveller contained in the machine travelling backward, while the time machine is an otherwise ordinary object sitting in normal space-time, travelling forward.