Well, PSIA does publish standard teaching manuals that, in some sense, establish their skill progressions and "jargon". They also have booklets of recommended drills/exercises and things like that. They do go around and demonstrate the latest and greatest 'stuff' to ski schools and instructors, but they don't try to force individual ski schools to teach in any specific manner. An individual ski school may make its instructors teach in a very specific way, but that's not coming from the central PSIA organization.
If there's anything they preach, it's that you should try to tailor the lesson to the needs of the student. Of course, the flip side is that you get complaints about inconsistency between instructors and ski schools. Because there's no rigid curriculum, the same student might get very different lessons from different instructors based on how they personally teach and what they see in the student's skiing.