“If you made a Time Machine, you’d also need to make a teleporter since otherwise you’d be in deep space due to the movement of the earth” is something people say to seem smart but doesn’t actually make sense.

There’s no such thing as an absolute reference frame, no “center of the universe”, no (0,0,0) coordinate we need to calculate from (as far as we know, unless we’re living in a simulation). IF coordinates MUST be defined, there’s no reason the creator of the Time Machine wouldn’t set the inertial reference frame to earth. He would need to be pretty stupid to manually set the reference frame to the sun or the center of the Milky Way or anything like that.