A Center Controller reported an aircraft descended below its assigned altitude and flew below the Minimum IFR Altitude.

Narrative

I was training a trainee on sector 5. The trainee was issuing an RNAV approach into GCD; and gave the pilot a clear and correct clearance. 'Cross (FIX) at or above 090...'. The pilot read it back correctly and then descended before that fix. I instructed the trainee to read a Low Altitude Alert to the aircraft when I saw they were 200ft below the MIA (Minimum IFR Altitude); and the trainee did not do so. They instead asked the pilot if they were level at 090. The pilot reiterated that they did in fact begin their descent early. I should have issued the alert myself to ensure it was done properly; and not allowed my trainee to ask the pilot a question like that. As for the MIA violation in general; there was nothing we could have done in regards to that. It was a pilot error to begin the descent early and they admitted as such on frequency. I am not submitting this report within the time frame only because I got locked out of my account and this is the earliest I was able to recover my password.