Splash ... I just had this conversation and I think boulderjohn has a valid observation .. a new diver is going to assume that a DM is going to do the same things that their DM did, and not going to know to ask about a DM's responsabilities
And for that I feel the instructor that certifies the students has a duty to inform their OW students that each and every dive operator has different rules and roles and that no two dive shops are the same.
If this were my class, on the last night of class before we all take out test I would review with my students the basics of diving. I would even go as far as to ask the class to tell me some questions they might have for me if they were booking a dive.
For example, if you certified a student and they went on a trip and had a horrible experience because things you taught them were different from how the trip went you're going to hear about it, right? Why not prepare your students and give them the information they need to make good decisions. Teach them to ask and they will.