I've not used Cole jaws like those, but I've used a Longworth chuck that follows a similar principal of holding the rim of the bowl. I also got whacked in the head by a bowl that came out of the Longworth chuck. Personally, I shy away from that type of jaws now that I've learned some other ways to finish my bowl bottoms (friction chuck or vacuum chuck), but there are a lot of turners who use Cole jaws and like them. (I wish I was in LA so I could show you a few ways I do it.)
I don't remember what type of chuck you have. If it's not a Vicmark chuck, I'm not sure if these jaws would fit.