Although I've never had shoulder or shoulder rotator cuff problems, I just irritated my shoulder doing squats believe it or not.
My form is proper, but it was the stupid bar supports where you put the bar on when you're done your sets. At the front of the 2 adjustable supports there is a little edge sticking up.
You either have to lift the bar off with your shoulders or adjust the supports below shoulder width apart so that when you stand up, the bar is well away from the supports.
I had it at shoulder level & on a heavy set I had to lift the left side up with 365lbs on my back. I felt my left shoulder make a slight wierd move.
Now my shoulder is sore to do shoulder presses.
I'm not used to these types of bar supports on the squatting cages as in my old gym the bar supports were just a flat surface that you could just slide the bar back on & off. But it's feeling better today.