That logic assumes that there is some universal way if measuring the position of the earth, but there is no absolute system for measuring position in space. Location, distance, velocity, and even simultaneity depend entirely on the choice of a frame of reference. And the frame in which the earth is stationary is no less valid than any other.

Also the type of time machine has a bearing here. The traditional H.G. Wells vehicle-type doesn’t jump, but moves smoothlythrough all the intervening moments in time, so there’s no reason it wouldn’t stay firmly on the surface. And a time portal that forms a connection to the same apparatus at a different time would have no problem either, since the machine itself doesn’t move except in the ordinary way.