Koha documentation says:
Superlibrarians will see modifications for any branch, other staff will
only see modifications for patrons who belong to their logged in branch.
However non-superlibrarian staff *can* see patron modification requests from other branches.
1/ In opac, create a self registration request at branch A.
2/ Log in to staff client as non-superlibrarian staff member with 'modify patron' permissions, at branch B.
3/ Note that 'Patrons requesting modifications' on Staff Client Home page will show a request.
4/ Click on 'Patrons requesting modifications'. You will see the request from step 1/.
See bug 10904, did you check the perf IndependentBranchesPatronModifications?
I have confirmed that this setting was the culprit. I believe Barton submitted this ticket on our behalf. We did not know about the setting. I am going to go ahead and mark this as resolved.