If it says acrylic resins on the paint, then that normally means "100% Acrylic" resins, which in paint speak means the Plexiglas type paint which have much better moisture resistance that the wood glue type paints.
And you're also correct about covering a general purpose primer. Once it's covered with a quality paint, it won't get enough moisture into it to cause problems with peeling.
In future, when it comes time to repaint your bathroom, remember that you can also get paints specifically meant for bathrooms. Not only will these paints stand up better to moisture and humidity, but they'll also have mildewcides added to them. These mildewcides are solid powders that dissolve in the latex paint. These mildewcides are so highly soluble in water that even the presence of high humidity causes those mildewcides to migrate through the solid paint film toward that humidity. Once at the surface of the paint, those mildewcides kill any milidew spores that land on the paint before they have a chance to grow. So, to keep a bathroom paint effective for as long as possible, it's a good idea not to clean that paint with water any more often than necessary because doing that accelerates the depletion of the mildewcide out of the paint film.
I'm sorry to hear that you drank that kool-aid and feel the need to spread the word.
I'm going to ask for plexiglass paint the next time I'm at the paint store too, they should get a good laugh out of that one.