So far, we don't know. It's almost like this universe temporarily - in some cases - overwrites this universe's counterpart to allow someone from the primary universe to come in. In the case of those from Genosha, it's different. Only a select few end up in the Tower, triggered by a locating and relocating spell over Genosha.
But we've had deceased persons arrive too, so that doesn't always hold true. I suspect something more ominous at play here.
I can conjure iced mochas. You can visit the Sanctum at 177A Bleecker Street in Greenwich Village.