The primer is bad! You're correct that the primer shouldn't smell like that. The drywall had no effect on the outcome, no worries there. Most likely the primer was old and simply rotted in the bucket(s). I have had PVA primer that smelled like this, too bad it wasn't noticed before application.
The only way to fix this is to reprime with a shellac primer, 2 coats. The painters could try oil base Kilz but it probably won't seal this stuff completely.
Ask Benjamin Moore what they are going to do about it and suggest they supply the new primer and some cash for fixing this mess.