Given that even in a "real" situation, it would be unlikely to have any significant effect, i think it's you who didn't quite think things through. There's a difference of at least two generations here. People aren't meeting their parents, they're meeting alternate universe versions of their grandparents.
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You're trying to avoid problems that have no reason to even happen. There's a thirty year difference in age, their MU versions kids already have families. Double ups and inbreeding are a non-issue. Double ups would have been a non-issue anyway. It's not like identical twins somehow can't exist in the same area. At most you need some sort of naming convention to keep them apart, but that's more of a bureaucratic thing.
As for why they come over? Because the MU Horde asked for help and these guys decided to follow the call. Your "solution" just makes the situation unnecessarily more complicated.