Given the speed the earth move through space I don’t see how you would get the space and time to align for materialization on a past earth.
I've said such many times regarding time travel in our known Universe. Not only does the Earth revolve around the Sun. The Solar System revolves around our galaxy, the Milky Way. Then, our galaxy is moving through the Universe at tremendous speed. Without the incredibly complex time/space computations, you could wind up in space or in the middle of another cosmic body and not the exact place you left on Earth.
There was a movie called, "The Philadelphia Experiment", when a Navy ship came back to its day from future time travel, and half the crew's bodies/atoms were interlaced with the atoms of the ship.
Again, time is a human construct. It is not malleable nor fungible. Doing the backward math of the galaxies' travel from the Singularity, time does not exist as a universal force like mass, electro-magnetism, light photons, and the unsolved physics of gravity.
As for parallel dimensions if they are not made up of our known forces, what are they made of? Pure energy? Hey, what do I know? Like I said above, that could explain UFO's. Question: If from a different plain of existence, why must they have so many lights on the outside that is witnessed? Or is that their cross-dimentional time-traveling power of propulsion?
Still think its physicists trying to reconcile their math equations with theories, much like climatologists with their models of global warming.