That would imply that I can go and get a check-ride with Melbourne Aviation in a Jabiru, then continue to fly that Jabiru into Class D Moorabbin without a PPL. I'm pretty sure it doesn't work like that.
The other operators, including the one I trained at, only let people they trained from ab-initio hire and fly. They would not check out random people for CTA and let them fly.
But once they have their pilot cert, (ie have "graduated"), won't they have to fly from Tooradin or Tyabb unless they hold a PPL?
See above.
Like I said: the rules are clear as mud. I am not saying what the rules are or how they should be interpreted; I'm just saying what those with the exemption are doing with it in the real world.