Obsession with people is something that I definitely experience. When I'm obsessed with a person, I think about them all the time, and make up scenarios involving them and spend a long time picturing them in my mind. I create idealized versions of these people in my mind, and am super disappointed when they don't live up to my expectations. There's an element of fear in it too; when I go somewhere, I am nervous that I will see my "think-about" (as I call the people I am obsessed with). This is going to sound really weird, but my obsessions aren't just with people; they can be with places as well.
I have no idea why I have them, or why other Aspies might experience similar things. I think I just have an obsessive personality (if that's a thing), since I tend to obsess over a lot of things.