assimilated into higher Chinese civilization, not other way around.

It adoped the new religion and new political system after conquering China, just like many European barbarians were Christianized after they had conquered Rome since 5th century.

They all became part of the so called medieval civilization.

Howeer, the mighty 元朝 (Mongols) failed so quickly in China in less than 1 century, exactly because it refused to be completely assimilated into Chinese civilization.

The Manchurian fared better, because they were almost completely assimilated.