I really don’t get why the time machine would have to do any calculations at all. The time machine is in this reference frame. You seem to assume that by going back through time you’d be teleporting through time, which leaves the open question of where you’d appear. However, I’d much rather assume that you’d actually be “going” through time. You wouldn’t cease to exist until you reappeared somewhere. Instead you’d be in the machine for some time until you’d get out of the machine again. That’d mean neither you nor the machine ever leave the reference frame.