No, the 15-minute tutorial is not timed. The students' time does not begin counting down until the exam begins. Also, a proctor cannot pause a student while they are in the tutorial. The pause function only applies to the actual exam.
Important: This could also explain why some students finish or time out 15 minutes before the rest of the class. The tutorial is optional, so if a student elects to skip the tutorial, their time will run out before the others.