I prefer a Cortesia that isn't a total wankage so territories more or less being the same as the old Aztec empire would be good enough. They would have to establish a government and all that wonderfully time-taxing stuff.
Yes, for the better part of the 16th century they'd be working on keeping the borders of the Old Aztec Empire, securing the more troublesome neighbors (Tarascans and Mayas), and keeping the Spanish from invading.