A Center Controller reported an aircraft approved to make a 360 turn deviated from its assigned altitude and flew below the Minimum IFR Altitude.

Narrative

While providing OJTI on the sector; Aircraft X requested the RNAV Runway 4 until they got the airport in sight to change to a visual approach. This was a plain language request made by the pilot which allowed ample time for coordination and planning. Traffic volume and complexity were low. When prompted; the Trainee started a track on a VFR aircraft who was essentially established inbound on the requested approach but not in communication with us as they were VFR without flight following. The Trainee called the traffic to Aircraft X and Aircraft X reported that they had the traffic in sight. Trainee responded 'roger'. Aircraft X then reported that they were going to do a 360 to get away from the traffic. Trainee responded 'roger' instead of specifying a direction of turn (suggested because of additional VFR traffic to the left at 3100. The radar Trainee said that he had never heard such of a request and didn't know what to do; despite having seen similar requests in school scenarios. After the 360; Aircraft X climbed then descended below the MIA triggering a low altitude alert. Encourage everyone that it is okay to ask for help and admit when they don't know something.