I have participated in the invigilation of self-taught exams several times, but the teacher does not change. Two teachers are always in charge of the same examination room for the same exam, so is invigilation in different places. Taking Yunnan Province as an example, the senior high school entrance examination, the college entrance examination, the adult college entrance examination and the civil service examination are all the same, and lots can be drawn before the examination, but rotation supervision is not implemented during the examination unless there are special requirements for the current examination.
However, the self-study exam is divided into examination rooms according to subjects, and each candidate needs to take different subjects, so basically few teachers invigilate the same group of students.