I'm pretty sure it's using "postbit_display_complete". But the problem is that when you quick edit, javascript on the page makes a call to editpost.php and gets back just the edited message area. So postbit_display_complete is not called, and also the place where the notice is displayed is not getting updated. I think you'd either need to figure out how you can get some javascript to run when the post is updated, so you can set the message, or else you could disable ajax features so that the page reloads, but then of course you're losing that feature.
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