Assuming there is only one version of us in the Prime Universe, then it would have to be that same one being drawn here each time.
And that is interesting to me because if this rift is completely random, why would it keep pulling the same people in after, theorhetically, tossing them back?
And if this rift is not random, then what is the purpose? We're needed? Why couldn't the original version of us in this fractured universe handle whatever crisis arises?