OK, I think I know what you are trying to do now. So, no, as far as I know, a user in one group doesn't have the permissions to see or work the tickets that belong to another group unless, as you've said, that user is in both groups. All users who belong to groups have a predefined set of permissions limiting or allowing them to perform certain tasks within ProcessManager but those permissions don't extend to permissions on allowing on group to see another groups incidents.
Example:
When I copy the permissions from Support II to NewGroup, NewGroup has the same rights inside of ServiceDesk meaning they see the same menus and can perform the same tasks as Support II but they still don't have the permissions to see or work Support II's processes (incidents, problems, etc.). Those permissions are set by allowing a worker to belong to more than one group.
I hope that clears things up just a bit.