Because Phacility implements auth by using another Phabricator instance as an OAuth provider, logging out of a Phacility instance does not fully log you out of the cluster (similar to how logging out of Phabricator wouldn't log you out of GitHub if you were using GitHub OAuth).
This is consistent, but somewhat surprising.
I think the best approach here is probably to add an option to the logout workflow to let the user log out of linked providers:
+--------------------------------+ | Log Out | +--------------------------------+ | Are you sure you want | | to log out? | | | | [X] Also log out of Phacility. | +--------------------------------+ | (Cancel) (Log Out) | +--------------------------------+
This is a bit involved, but relatively generalizable.