The activities … in categories visible to the groups that both “members” and “everyone” simultaneously belong to.
The crux of the “problem” is that it doesn’t really make sense to post “as a member of such-and-such a group”; one posts rather “in such-and-such a place,” which is reflected in the UI.
! Advanced search: posts from members of a group - #3 by JagWaugh
Perhaps this is partly a solution:
https://your.domain/search?q=category%3Acamille%20group%3Acamille