Let's have our cake and eat it too.* Different universes, alternate universes and different quantum realities are all the same thing. Each one has its own quantum signature. An altered timeline skews off from the original, creating its own quantum signature as it does, so any travel between universes can be detected by those that are looking for them. Kirk and company would have been detected because they were from a different quantum reality.
'Old' Alexander or 'old' Arne Darvin either would or wouldn't, depending on how time played out between now and the future they come from. But it's actually unlikely that they wouldn't, because of the theory that by coming back in time and at least attempting to make changes, they are creating a new alternate universe. Each change they make causes a new quantum signature to be created, and they actually have no guarantee that when they go forward they'll end up in the same universe they started from.
*That's actually supposed to be "Eat cake and have it too" but that's irrelevant.