You're not selecting the right objects for the report and as a result you're creating a cartesian product. The supervisor field you're using doesn't have nothing to do with group managers, unless your setup uses this instead of the regular group manager flag in the group memberships table.
I don't have a test setup with the OOB universe available so I'm going out on a limb here and attempt helping you without actually testing the results, but I think you need the fields [Request Detail].[Ref Num] and [Request Detail].[Group Name] as the result objects and then in the filter section you need to create a subquery where the first field you drag the [Request Detail].[Group Name] and in the second field you drag the [Contact Detail].[Contact Extended].[Contact Grpmem].[Group Name]. Then in the filter section of that subquery you add [Contact Detail].[Contact Extended].[Contact Grpmem].[Manager Flag] = 1 and [Contact Detail].[Contact Extended].[Contact Grpmem].[Member Combo Name] like you want it to be filtered.
Be aware that a group can have more than one manager and a manager can manage more than one group, so you might get overlap with the results for different group managers.