The first time the Dai were really ruled over by the Chinese was during the Yuan dynasty, when Mongol conquerors managed to capture as far south as modern day Burma. The subsequent dynasty, the Ming, pushed the Mongols out and began encroaching on Dai lands, producing a series of ongoing conflicts between the Dai and the Han Chinese that would come to a head in 1874 when a Hui Muslim named Du Wenxiu united the Dai with other minority groups in a rebellion against the Qing dynasty.
The Communists tried to make reparations with the Dai, establishing Xishuangbanna as an autonomous prefecture in the 1950s, but many Dai still faced persecution during the later Cultural Revolution and fled across the border to Dai communities in Thailand, Laos, Burma, and Vietnam.
I am 100% dai.