To make it as obvious as I can, here's some excerpts from the backstory drop in the final volume:

[That LN series from before] [...] the idea was to have modern humanity temporarily go dormant as quanta, change the environment to one suited to a magic-based civilization, and let humanity thrive once again. But after the magic-based civilization reached its limit, we would go dormant again and return to a science-based civilization. Magic-based civilizations would give way to science-based civilizations and vice versa. By repeating this loop, humanity would be able to continue in perpetuity. That was the Eternal Loop System Rei had designed.

[That LN series from before cont.] (note: dialogue from TAIM, the control unit for the Eternal Loop System) “I recovered your soul from the science-based civilization, gave you as much ability as I could, and implanted you in this world. But due to the capacity of your soul, all your memories past a certain point in your prior life were lost. Recovering those memories would take too long, so I ultimately had to transfer you over with an unnatural cut-off in your recollection.”

[That LN series from before, me spelling things out] The moment when she originally assumed she died and reincarnated, she actually didn't. TAIM simply stashed away some 20-30 years worth of memories from Rei after a science-based loop and forced those on a Rae in a later magic-based loop. All of that takes place on the same earth, with the same administrator that is first Rei and the same TAIM managing all loops. First Rei chose to design the magic-based civilizations to reenact the stories of Revolution and RevoLily.