Is there some way to add trim to cover the gap?

" Today when they installed our countertops they said that the sink was pushed too far into the cabinets and was supposed to stick out further than the lip of the countertops."

They are wrong. On a self-rimming sink, the back of the apron kisses the cabinet front. Period. If the top sticks out past the sink, have them clip or round the protruding corner; it will look fine.

If the tops have been installed, they'll have to recut, profile, and polish the rear of the cutout to get the proper reveal which should be slightly positive as shown. The sink or the countertop will have to be pulled for that to happen. Let's hope the faucet holes haven't yet been drilled or they may have to be filled or the rear rail replaced.

The cabinet is cut correctly. If the cabinet wasn't relieved as shown, the radius at the sink flange/apron wouldn't allow the rear of the apron to touch the cabinet front.

"You do not do a cut out for a self trimming sink. It slips right over the frame. Now that has to be rebuilt, and the sinks installed correctly."

Cabinets always have to be cut for an undermount apron sink installation; self-rimming or not. You have to relieve at least the thickness of the flange. On a short apron retrofit, the top rail and the center divider (if there is one) are removed and the cabinet relieved for the flange.

Thank you! that is much easier than rebuilding the cabinet. the countertop installers have already drilled the faucet holes but we will just tell them that section of the counter needs to be redone with a new slab.

It depends upon where they drilled the holes.