The Triple Alliance governed their empire indirectly; you can say that it was sorta similar to the Achaemenids of Persia. When the Mexica conquered a city, they tended to leave the local ruler in place, provided that that they send their tribute to the imperial core. Azcapotzalco could govern in a similar sense or it might govern more as a traditional empire, leaving governors to rule its conquered subjects as opposed to leaving local rulers in place. As Huitzilopochtli was the patron god of the Mexica and expansion had a religious basis to it, I expect a slightly lesser emphasis on mass human sacrifice.