Even though it's a different process, there's nothing that says it can't be the same entity doing both.

But I have to admit, the idea of the eggs being from a similar world is interesting. Most people who arrive here become human if they weren't already, don't they? What if there's a world just like this one, but without humans? In that case, the Pokemon are probably the most intelligent creatures. So if the criteria for being pulled here is being one of the most intelligent species in a given world, then it would make sense for Pokemon to be pulled here as well.