Correct me if I'm wrong, but Japan exerted political hegemony for only around 40-45 years, largely over Korea, whereas both pre-modern Korea and Japan lived under significant Chinese influence; both of their traditional scripts are just Chinese.
Japan was never occupied by a regional hegemon. There was significant influence on Japanese culture from China during a few phases around a thousand years ago, but those were borrowed ideas that were mixed with local religion and philosophy to form something uniquely Japanese.
The situation with Tibet is similar. Unlike Japan, Tibet was subjugated by hegemonic powers at various points. But Tibetan culture is quite unique and resilient. It really wouldn't be fair to say that Tibetan culture is derivative of India, China, or steppe peoples. They took Buddhism from India/Nepal, but made it into their own. They've kept their own language and culture.
And where does Vietnam fit? Religion and architecture from India. Writing and legal system from China. Food and spoken language are distinctly south-east asian.
I really don't think you can slice up Asia to be either 'India' or 'China'. It's way more complex than that.
