The Inca did not convert anyone. Their expansion laid a state religion over local religion, and the two operated at different levels.
The state cult centred on Inti, the sun, whose principal temple stood at Cusco with its walls plated in gold and whose service was supported by dedicated land, herds and labour. A high priest presided. The aqllakuna, women selected in childhood and removed to enclosed houses, wove cloth and brewed maize beer for the cult and were also bestowed in marriage by the state. Viracocha, a creator figure, Illapa, thunder and weather, Mama Killa, the moon, and several constellations all had a place. The Sapa Inca was held to descend from the sun, which made obedience to him a religious matter as well as a political one.
Local religion was older and largely untouched. Every community had its huacas (a spring, a rock formation, a boulder, a field, an object, a mummified ancestor), and its own founding ancestor and place of origin. The Inca strategy was incorporation rather than suppression. Local huacas were ranked within a system radiating from Cusco, the sons of provincial elites were educated in the capital, and prominent cult objects were installed there. Conquered peoples continued their own observances, and when Inca power collapsed those observances remained. That is a large part of why the state cult vanished within a generation and the rest of it did not.
Cusco itself was organised religiously. Lines described in colonial sources as ceques radiated from the sun temple, each strung with shrines assigned to particular kin groups for maintenance and offering. The system is known from a seventeenth-century description drawing on earlier material, and its details are debated. What it indicates is a religion mapped onto landscape and onto social obligation rather than gathered into congregations.