There could perhaps be some special handling that I haven’t seen so far, but if not then I would assume that using the ‘submit’ html option should have no effect, since I would imagine that submit is actually destined for a form, whereas you are merely making an anchor.
If you want to have an ajax submit button, then either you will need to make a form, and add a javascript handler to something either to handle the submit or to trigger it (making sure that you cancel the default action and submit by ajax), or you just add a link, and add some javascript to it to send an ajax form on click.
I personally prefer the first option since it degrades gracefully when Javascript is not enabled.
It can indeed generate an ajax form, but I think at the very least you’re going to have to add some kind of ‘params’ array to specify a POST rather than GET submit.
Otherwise, you can just copy the delete method used by CGridView (removing the gridview references of course) from CButtonColumn.
But you are still not using a unique id in your ajax example. If you don’t define your own ids for the html element you create then Yii will create a random one. The problem is that it often duplicates ids when elements get loaded via ajax (like via pagination etc.).
EDIT2: Why are you reloading the page on success? Couldn’t you just render the new list partially server side and replace it via “update”=>"#yourlistid"