Hmm. They were already here in this timeline, not in another. It means that wherever they were in this timeline, for whatever unfathomable reason, they were drawn here to this city. It's this timeline's selves that are being drawn here.
Essentially? Yes. The other...let us call it the "main timeline" universe that we're from, seems more stable and has our counterparts in it. You're still you, everyone else around you is still them. When time split, branching off from the same universe, it created you's and two of everyone else, and everyone wouldn't ever know they were anything else but themselves, and have identical sets of memories and experiences. Complicating this, there's literally countless versions of all us all, in vastly different variations and living in vastly different circumstances, throughout the Multiverse. Time branches off more than we imagine it does. There's one where the Nazis won WWII, and the timeline went on from there. There's even one where the Chitauri invasion was successful. I've seen some of these. Not recommended viewing. Each are like branches on a massive tree, each becoming a timeline all their own.
Even if concepts of time can get profoundly messed up trying to explain all of the variables and possibilities, these are good questions to ask. It does make for good stories, just not the ones you probably wanted to live through.