I did my DM training in SSI about a year and a half ago. There was no internship. I think people just do that for experience because it is not required by SSI standards. My training was three weekends, and one of them was optional (helping out with the pool sessions of a OW course), plus the SSI e-learning. The training for SSI DG/DM and instructors is pretty minimal, really. You don't go over a bunch of new skills or learn new ways of diving because you are required to have taken several courses (Science of Diving) or have the logged experience in those areas (Night and Navigation) as well as have a minimum number of dives and hours under water. It's really more of an evaluation than training. They want to make sure you are going to represent yourself and SSI well and that you have the necessary skills underwater, then they teach you a little about the SSI teaching process.
What you are required to do depends on who you work with. I live a few miles from the shop and have to drive right past it on my way to the quarry that we do check out dives in, so I tend to haul out the O2, first aid, AED, etc., as well as grab gear for students who can't or forgot to pick it up beforehand. With some exceptions for age and disability, we require students to haul their own gear once we are on the site. I have occasionally filled tanks between classes that I was teaching if we had a lot of students or classes going on simultaneously and swapping without refilling on demand wasn't an option. Otherwise, I just teach - I'm not even required to clean up after my classes. I just have the students drop all of their COVID soaked rental gear (hopefully I'm just joking) into the decon tank and the shop's retail associates take care of the rest.