I am a little confused. If you don't want the user A to see user B's changes until the refresh and you're just looking for user B making changes to update their with a "submit" then, yeah, an AJAX request is all you need on some event (like when the focus leaves the input box).

If you do whant user A to see what user B just updated, then you can look into:

• pub-sub pattern (publish/subscriber)
• YUI3 has/had this thing they called PJAX, which was like AJAX, but was geared towards progressively enhanceing the HTML on the page - so selectively updating DOM elements as the state of the experience evolved

Note: YUI3 is dead, but they came out with some interesting ideas and were thought leaders before this explosion of JavaScript libraries. This may or may not be what you're looking for, but it will help you narrow your search results by seeing the jargon that comes with it.

Also, if you're looking for a "google docs" experience, the you may want to look at etherpad's source. It's not Perl, but they provide some "collaborative edit" features that seem basic enough to show you one such approach.