That's not a concern. At that level, you need to be "type-certified". It's not that they are training on Airbus aircraft, it's that "to operate Airbus (or Boeing or Embraer), you must train on Airbus (Boeing, or Embraer)".

In addition to type certification for a pilot, each airline will then layer their SOPs on top of that, the "this is how -we- fly this aircraft on these types of routes".