I'd say the hypothesis is modernity-centric, which might be equivalent to saying it's centered on Europe, as you point out.
One main division is between the kind of liberal republicanism that only modernity makes possible, and the premodern civilizations, most of which were autocratic. Another division is between civilization and nomadic egalitarianism. The latter kind of "socialism" for smaller, less civilized, or non-sedentary groups would be explainable in pragmatic terms.
Anyway, it's true that I haven't yet dived into how this hypothesis fares when considering the finer distinctions between premodern large societies. I've assumed they're all relatively autocratic, compared, say, to modern Europe or North America.
But if you're talking about the lack of autocracy in small nomadic groups, that's another story. This hypothesis is meant to apply to large societies.
Regarding the Tupi, I'm not sure we should consider them socialists in any utopian sense:
"According to primary source accounts by primarily European writers, the Tupi were divided into several tribes which would constantly engage in war with each other. In these wars the Tupi would normally try to capture their enemies to later kill them in cannibalistic rituals....Most Brazilian scholars, however, attest to the cultural centrality of cannibalism in Tupian culture."
Also, although there were around a million Tupi in total in 1500, "They were divided into tribes, each tribe numbering from 300 to 2,000 people."
