The wikipedia article as well as scientific papers like Janusek 2002 and Ortloff and Kolata 1993 treat the historical existence of the Tiwanaku empire as a fact without offering any evidence corroborating it.
The papers are not open access (sorry for that!) but the perspective becomes clear from the abstracts. The papers go on to discuss archaeological evidence for settlement patterns, technology, artifacts etc etc.
I understand that archaeological studies may offer solid evidence of a culturally and technologically advanced civilization, but how can it be established that this civilization constituted a state or empire?
Pre-Columbian cultures in South America had (almost certainly) no writing system, so contemporary historical accounts do not exist. Is there perhaps evidence from later historical sources?
I had a brief look at (an English translation of) Guaman Poma's "The First New Chronicle and Good Government" written by a member of the provincial Peruvian Native American nobility. He gives the probably earliest comprehensive account of Incan and pre-Incan history of the region. However, what he produces in his chapter on pre-Incan history ("Chapter of the Ages of the Indians") is a rather bizarre mix of biblical narrative, contemporary Spanish Christian philosophy and native American mythology. Other historical sources are probably similar.
In any case, I fail to see any historical value in this particular chapter of Guaman Poma's work - but maybe historians disagree and manage to squeeze something useful out of it? Or maybe, there are other more informative sources?