Deleted user from subsite can still login (wordpress multisite)

I have a problem with Wordpress Multisite.

When I delete a user from a subsite, the user is deleted in the subsites userlist but he can still log in. I dont want this, he should be deleted and denied access.

I checked in the network userlist and he is still there. So i guess this is why he can login. So how do you let an admin (not super-admin) delete a user so he dissapears from the site completely? Or at least how can you stop that user to be able to login to the subsite? I mean, he is deleted from the subsite, he shouldnt be able to login to that.. I want the subsite Admin to be able to controll their users (add and delete) without help from the Super-admin.

Really appriciate all help, I have made a lot of research but I cant find anything that solves my problem.