I always assumed they are like heads of house/teachers in terms of their ability to punish or reward, and they handle the pastoral responsibilities of students the way Modern teachers would but Victorian teachers definitely wouldn't have. Meserimus isn't talking to a female student about her monthly - not even if he is related to them!

that's what the matrons did in my school! lol They were treated as teachers but with a school counselor/pastoral care mandate for boarding students.