Surely there can't be other universes with different timelines if people have had proven micro time jumps and weren't disappearing or duplicated

The old age question about grandfather paradox where if somebody goes back in time and kills their grandpa, how can they exist? this was attempted to be answered by doing the crazy act in alternate world theories therefore not canceling their own existence, however, what I don’t understand is if traveling through time puts you in an alternate universe then where would the threshold be set? People on the upstairs of a building travel through time faster than people downstairs since they are closer to the central point of gravity, which is the earth’s core for us. Wouldn’t astronauts who jumped slightly ahead in time just simply vanish from our existence and there would be two versions of them somewhere else if this theory were to be true?