A TRACON Controller reported they received a Low Altitude Alert when an aircraft descended below a crossing restriction on an approach.

Narrative

I was working ZZZ radar combined at the X sector. It was just before XA:00 local time. I only had 2 aircraft on frequency and had not been on long. Traffic was not complex. The only abnormal issue with the traffic was the amount of Medevac aircraft that were in and out of ZZZ. I had an IFR Medevac asking for the RNAV Y approach to Runway XXL. I issued a proper crossing restriction for the fix pilots typically use for the approach. The pilot correctly read back the altitude; but did not stop at the issued altitude. I have great confidence in our Medevac pilots so I was not concerned that he might miss the altitude.A few minutes later; the Low Alt alarm went off. I issued proper low altitude phraseology and the pilot responded with 'correcting.' I then pointed out the airport and the pilot reported that he had the airport in sight. I then cleared him for a Visual Approach to Runway XXL. The pilot landed without incident. I decided to file this [report] to satisfy my need to report the issue and to protect myself. I made the decision NOT to issue pilot deviation phraseology and force this incident up to management. Our Medevac pilots are always extremely professional and do an amazing job getting medically critical passengers in and out of ZZZ quickly and safely. I had no desire to expound the issue and maybe take a good pilot who just made a mental error; out of the sky. I have no doubt that the pilot knew exactly what he had done wrong and I believe he will correct the issue. I have no recommendations for this. I issued a good altitude; and got a correct read back from the pilot. I'm sure the pilot was probably just tired and I have no doubt that he will correct this problem.