Yeah, unfortunately UNA's subscription items don't have an automatic unsubscribe coded into them.
If you have members that subscribe and then want to unsubscribe, you have to manually go in and stop their subscription to your site. It works the same way with the modules, as they (UNA) will have to go in and manually unsubscribe you from them.
I've mentioned this to them and asked them if they can add automation to this process already, but it hasn't happened yet apparently.
If they're paying members, you have to manually go in and unsubscribe them from what ever payment method that they're paying with too...which is kind of a pain because honestly I feel that should be automated too.