Everything works well.
However, the Member Map tab at the top does not appear to follow the Application level or Menu Level permissions.
If I have only Admins being able to access it at the Application level, the tab is still visible to other groups. In fact, other groups can click on the tab resulting in a "You do not have permission" error page. Setting it to only be visible to Admins within the Menu level results in the same thing.
If a group does not have permission to access the application, then the application tab should not be shown to these groups.