C172 Instructor reported receiving conflicting ATC clearance in the traffic pattern followed by a NMAC event.

Narrative

While on downwind to Runway XX; we were advised by the tower to follow the C-172 aircraft in front of us. As he turned base to final; the student started the base turn upon which the tower instructed us to perform a 360-degree turn. The student rolled out from the 360 on base and shortly after he was told to make another 360-degree turn on base. Upon completing the 360-degree turn he was requested to turn downwind for traffic that we had not heard about; and no description of the traffic was given to us. Upon turning downwind; a Pilatus PC-12 passed us 300 to 400 feet on our right side; and he was not talking to the tower. After the Pilatus passed on our right; he started talking to the tower and requested clearance to land. Tower instructed us to follow the Pilatus for landing #2 Runway XX.At no time did I hear any radio traffic between the tower and the Pilatus until he passed us on our right at which time he communicated with the tower for clearance.After landing; ground control asked the student if there was an instructor at which time ground asked me what transpired on final. I advised ground that we were told to do two 360 -degree turns and extend the downwind.