The knight model depends on how many dragon slays you get in a row without dying:
Esquire (Pink: Starting rank.)
Knight (Green: Turn off the Dragon once.)
Baron (Blue: Turn off the Dragon twice.)
Count (White: Turn off the Dragon thrice.)
Birb will spawn a while into the round. When he does, the Knights can pick him up and throw him at the Dragon once to stun it. If Birb is thrown at the Dragon twice, it will act as if the button has been pressed and the Knights will win the round. You get units/credits for stunning the Dragon with Birb.
all info is from this guide: