CBSubs does not manage usergroups it's not configured to manage. For it to add/remove from Registered you'd need a CBSubs plan that does that. However, I don't recommend removing them from Registered. Your custom usergroups should ideally be child groups of Registered as well to ensure permission inheritance. Example as follows.

Public
- Registered
- - Subscriber

In this case it's fine for them to both be Registered and Subscriber. Subscriber usergroup should give access and not take away access so there should be no issues by doing this.

Your alternative would be to use CB Auto Actions to give more control over usergroup management where it can completely replace all their usergroups with your single Subscriber usergroup.