I believe you said you “pushed” your cylinder all the way down. The 88 calipers need to be screwed in, to compress the caliper. I used a tool made specifically for this job. You should be able to pick it up at any automotive parts store, plus it’s pretty cheap. It’s just a little square metal tool that you place on the end of a socket wrench. It should have little prongs on each of its sides.
Anyway, I recently installed the cavalier rotors on the rear of my 88 coupe and it worked out just fine, new brake pads too. The only problem I ran into was that the dust shields were rubbing up against the new rotors. A little gentle persuasion and I was good to go.
Hope this helps, good luck