Right. You don't "hit" a rivet with a squeezer. For starters, take out a rivet that you will want to squeeze. Just the rivet, say AN426AD3-4 (or whatever's appropriate for your practice pieces). Set the rivet on the workbench. Now grab your squeezer with the dies in it, connect it to air, and pull the trigger with nothing in it, just the squeezer by itself. If the two dies touch, open the adjustable ram (make it shorter) so that at full travel, the dies don't touch. Then open it some more, so that at full travel, the dies are apart by ALMOST the length of the rivet sitting on your workbench. You want the die gap to be a little smaller than the rivet, so that squeezing starts.
Now put the rivet in the hole of the parts you're assembling (scrap first until you get the hang of the squeezer). Set the top (non-moveable) die of the squeezer against the manufactured head of the rivet. Try to hold the squeezer as square to the part surface as possible, and slowly "feather" or gently depress the trigger of the squeezer, so that the ram gently closes. The ram will come up and ever so slightly begin to deform the rivet, and you will depress the trigger more and more until it reaches full travel and the trigger is fully depressed. The squeezer and your hand stay in the same place this way.
Remove the squeezer and close the gap between the dies just a little bit, and repeat. You want to sneak up on this setting. Soon you will have rivets that look like the photos that others posted.
You will begin to get a feel for your particular squeezer, the trigger feathering and the gap required for various rivet sizes. Then you can play tricks like holding the moveable die against the shop head and letting the non-moveable die come up to squeeze the tail of the rivet, for areas where access is an issue. You will see that the entire squeezer and the hand holding it will have to translate toward you while using this method.
Some pics of your squeezer and the "crepe" rivets with mangled aluminum would be helpful in diagnosis also.