CB Invites and Groups

I am using a number of groups formed by using the group field in user management. My plan is to have separate closed groups of users. Things are going well, I have figured out using separate menu links to let members only see their own list of users. But it seems that CB Invite works fine, invites new users but does not put them into a group or ideally the group they were invited from. Am I missing something and is there the possibility of making an invite put a user into the group that invited them? Now using 1.9.1 and Joomla 3.x

CB Invites has nothing to do with group assignment. It just sends them an email to come and register on the site.