Upvote:2
Well, here's what Wikipedia currently says on the subject:
There are many theories about the type of Tiwanaku state, one opinion is that it was a far-reaching military empire, while other theory is that it was the center for regional religious pilgrimages and llama caravan trade routes without much political authority. The Tiwanaku empire was most likely a result of direct colonization of nearby areas and cultural dominance over more distant areas, where Tiwanakuβs influence was based on religion, culture and trade instead of direct military and political control. The empire was more like a federation of autonomous regional communities for whom Tiwanaku was the center of religion, culture and trade.
So basically, there was clearly some kind of joint culture within that region, centered on Tiwanaku. But they don't know if it was a full on military empire (like say the Asyrian empire), or more or a colonial-type relationship, like the 8 BC Greek Diaspora.