Many times they just LOVE to be near you watching while you do stuff. Nerd used to sit on the desk drawer to my computer and watch, snooze, get scritches, etc.
Lurch would fly after me like a feathered puppy when I left the room, Dobby has chosen my sister so he loves to sit on her knee at the couch and fly after her any time she moves and plop on her shoulder. eventually she may try to feed you and finger wrestle with you too, that's pretty normal for them once they have chosen you.
Enjoy your new best friend.