The Quechua-speaking Huari had an empire, and Tiahuanaco a kingdom; both failed. From these ashes, new kingdoms arose. One came from Cuzco, near the Titicaca. Their incas became emperors. We're mainly quibbling over dates, also spelling because nowadays the sorts of idiot talking about ancestral-wisdom make a point of rejecting Spain's spelling.
We owe our account of events to Miguel Cabello de Balboa. By "we" I mean John Rowe in the 1940s. Radiocarbon wasn't a thing then; and, as we all know, radio-all-of-it got (badly) adulterated after those late 1940s - 1960s radiation bursts. Lowe was still adamantly pro-de-Balboa up to 1997, when radiocarbon recalibration started to work against him.
Frankly I don't consider Lowe to be in the same rank, in archaeological hell, as Thompson for the Maya. Lowe had every right to question radiocarbon. I do that here on this blog all'a-time.
"Lizzie" Wade is relaying that our calibrations have been getting better, even for the understudied Southern Hemisphere. Dendrochronology is coming online. It can peg New Zealand eruptions with world-spanning Carrington events. The Incas had access to vast quantities of wood from the upper Amazon and their northern and southern trade-partners.
Also, I'll have to concede here, de Balboa's account of events reads a lot like Livy. Rah-rah, our people fought these people, we won; on to the next battle. Also it is north-focused. The Spaniards could appreciate this on account those are the provinces they reached, first; also those regions had the most-recent experience with the Inca. The main languages up there were Quechua dialects. Cuzco - the Inca hometown - is about where begins another language, of the Aymara.
One large difference here is that South America didn't really have a Tlaxcala, or even a Texcoco, to record rival versions of events. Also - as Wade notes - nobody could write over there (can't really say "down there" for an Andean society); Mesoamerica was intensely literate.
Lowe, I think, could have stood to shown (if that's grammatic) more humility. He had no reason to defend the honour of de Balboa, which was really the honour of the Inca court; save inertia. If anything Lowe was too solicitous of ancestral-wisdom. Wade is pointing out that the incas were colonialists too, just like the Mexica "Aztec" hoped to be.
The new map has the Inca concentrating south of Titicaca. A rampage occurred in the south over the last decades AD 1300s: the far south, as in present Santiago. Then, the Inca turned north: around ~1400 (same time as Chincha), they hit Saqsaywaman. They did major construction at an exact date 1418 (dendro?). That's about when serious Inca remains also make serious inroads into the old Tiahuanaco environs. Over the ensuing 1400s the Inca faced a stubborn resistance at (southern) Copiapó, which - Wade says - got resolved when the Inca took the copper-mines and left alone the villages. The northern push against old Huari / Quechua homelands did happen, but (to me) that looks like it happened over the 1440s.
From 1450 on, I suppose the Tahuantinsuyu was being consolidated, in particular a new focus on Quito. Perhaps, as Bayes might suggest, the Spaniards found peoples who indeed had only recently joined the Inca Empire. That made easier to peel them off.
I have to admit, I find the new map difficult to interpret. Warrior-caste of Aymara hardened at the Mapuche frontier? Summoning the old Tiahuanacis out of caves?