The ancient south american cultures have gone through many cultural shifts throughout the last couple thousand years. The aztec civilization was actually a very minor player early on in central american history, they were so defeated and beaten that their enemies left them to die on the Tenochtitlan lake. The aztec were very ingenious people though and they founded the basis of hydroponics today using raft systems to cultivate food. When they expanded their empire they still kept their water based capitol and even today food is cultivated in the nutrient rich water of the Tenochtitlan lake. I don't know if they cultivated cannabis on it or not, but if they smoked it in their early exsistance on Tenochititlan then they most likely grew it hydroponicly.

As to "their herb" it's not their herb. Cannabis isn't native to the Western world. In fact cannabis was taken from present day india, and nepal to be propagated all the way throughout asia and onward accross the natural land bridge that formed between present day russia and alaska. Cannabis moved throughout north america with the nomatic tribes and later down in through central and south america.