The Aymara were one of the many Atlantean tribes which were conquered by Tawantinsuyu during the centuries. After in 1553 plagues hit the Inca empire, killing a great percentage of the population, the Aymara and several more (like the Chibcha) became practically independent again.
The Inca didn't like this, and looked for a chance for reconquest. During 1677-82, the Inca defeated the Aymara, reconquered the former South of their empire, which was stretching to OTL Chile / Argentine now again. An Uprising of the Aymara 1707-10 was defeated by Tawantinsuyu, and the Aymara were displaced to the Southern tip of Atlantis.
During 1826-29 however, emperor Alessandro I (who was lacking money) attacked and conquered the Inca empire. Aymaria became quasi-independent, although they had to become a protectorate of Britain.
After the anti-British War (1832-36) however, this changed too; since their land was unintersting for the victors, Aymaria was now free, and the only remaining native state in Atlantis.