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What if it's pulling a Jirachi but instead of pulling from places around the world, it pulls from all possible realities
Pokemon had a confirmed a multiverse since gen 6 and outright spelled it out since gen 7.
You straight up go to a universe where the ultrabeast incursion resulted in the destruction of the world, years later at that.
So previous titles have shown:
>alternate universes
>time in these universes are not synced
The turtle could have just yanked the professor from another universe that was years behind and the "time machine" yanks the paradox pokemon from a universe where those pokemon are actually a thing at that particular point in time.