In the group you have created make sure that all the members of that group are added to the group.
 example: all customer support group members inlcuding the supervisor/manager.

Now with the Group profile open assign the supervisor/manager as "Group Manager" of that group.

The supervisor should now have access to that groups call, now hear is the reason he still has access to the whole system, the privileges assigned to the supervisor is for more than just his group.  So a good practice is to create profiles based on the group or use the default "Team Leader/Supervisor" profile.  Do not add the profile to the individual user,  while in the Group click on the "Managers Profiles" tab and "attach Profile" use the wizard, click next, once you get to the available profiles select the profile you created for that group or use the default "Team Leader/supervisor" profile.

You may want to remove all the profiles attached to the supervisor/manager prior to doing this.  When you make the supervisor/manager a "Group Manager" of that Group it will automatically give them the "Managers Profile" privileges.  This will then only allow him to access only the members in the group.


So in the Managers profile tabs you should only have something like:
1. Basic Colums
2. Team Leader/Supervisor

or if you created a profile:

1. Basic Colums
2. Customer Support Supervisor