@jaxx I'm not sure what kind of type codes that site is using, but it doesn't claim anywhere they are ICAO codes aside from using that key in the URL (which might just be a result of legacy code).
The official ICAO codes are:
P28R - Arrow III
P28T - Arrow IV
P28S - Turbo Arrow III
P28U - Turbo Arrow IV
P28A - Warrior
The fact that these come from the official ICAO website should remove any doubt as to which site is correct