It depends on what “China” one refers to.
Remember — China was ruled by several dynasties, one overthrowing the other.
For 70 years China was ruled by the Mongols under Genghis Khan, Kublai Khan and their descendants. The Chinese called this “Yuan Chao” ( The Yuan Dynasty ).
So, was China undr the Yuan Dynasty, China then ? Or do we consider Mongol ruled China, not China?
For about 50 years after Mongols subdued Goryeo kingdom. This is subjective because Korea did still have nominal king and he did have absolute authority on Korean peninsula - but this king was almost more a part of Yuan court than an independent king - they were all married into Yuan imperial princesses and even grew up in Yuan court in many cases.
Mongols of course aren’t exactly Chinese (90% of Chinese are of the Han race), so that’s why it’s subjective, if you’re a Chinese person of Mongol descent then the answer is a yes, sort of.
At no time, prior to 1949, did China (any China) have any type of rule over Tibet. They of course say differently.