It might also be because you’re an admin, and thus have local moderator powers everywhere.

You would ban bob’s post from being shown on your instance’s copy of the federated community.

This happened recently, where a prolific user on !noncredibledefence was instance banned on blahaj.zone. if you visited !noncredibledefence@shit.just.works from blahaj.zone, none of his posts would be shown, but they were otherwise visible on other instances. I suspect in the case you’re talking about, it would only apply to the community on question and bob’s posts in other communities would be unaffected.