I'm in DM training right now (NASE) and my instructor doesn't really care what we use for training dives since it's what we're going to normally be diving anyway. But if we're assisting with an OW class, he at least wants us in something close to what the students are wearing, especially in the pool. We are of course welcome to use the shop's gear both at the pool and the lake if we want, which is all jackets and short hose primaries w/ longer octos. I'm just using my back inflate Zeagle with a 40" primary and standard octo during OW classes, but I may change that up and use a jacket to set more of an example for students, especially with regards to buoyancy, etc. Much easier to get better buoyancy and trim in a back inflate and that's not what they're learning in so in the interest of solidarity I may go back to basics. Not like I can dive my ffm during an OW class anyway.
I would think whatever shop you're DM'ing for would want you to use equipment close to what the students are learning in so you can set an example for them. For me, like I said I'm allowed to use a back inflate and whatever hose configs I want, even a BP/W if I choose. As long as when I'm helping with an OW course I'm using gear that the shop sells since I am in fact acting as a representative of the shop as their "employee." And that works out okay for me because I actually like my LDS and part of my reasoning for becoming a DM is to give something back. I've bought all my gear from them and they carry pretty much all the brands I know and trust. Not to mention they're starting a tec program and already carry a few different brands of "tec" gear and may be getting more soon. Not to mention as a DM for them, I get a pretty decent discount on all my gear, too, so that definitely helps.