Well duh, aren't they all?
Contractions, that is. Yes, they are: "He's" can be a contraction of, f'rinstance "He is", and "she's" can be a contraction of, among other things, "she has".
And "Joe's" is a genitive-s "contracted" onto Joe to indicate that we're (that's one too! And so's that! And that! :-) talking about something OF Joe's, probably (judging from the similar treatment in writing) descended from some ancient "Joe Hathes" or "Joe Seins" or something.
All of which doesn't matter: What matters is, Karsten's "Y'all's" was _not_ prima facie _a plural_, as he claimed (and it may well have been *intended* -- but didn't come out -- as) in his apology, but, as you so rightly note, a contraction.
Sure, I misread his original post and somehow got the impression the contraction in question was correct there, which it clearly (in retrospect) isn't... But what does that have to do with you telling me that it *is* a contraction -- where did I say it wasn't?!?
