Stopping rust under paint?

The guy who painted the car cut/welded the previous rust spots, but I guess its a wasted effort if he doesn't coat the back of the metal with anything :???:

I'm just hoping theres hope to stop it from getting any worse by use of a rust converter/air tight coating. Any recommendations?
the problem is he didn't cut out and weld in patches far enough, yha gotta cut out a few IN (or more) around not just the area thats showing.