India entered the modern era as a colony of Britain, and as such inherited colonial borders not whatever imperial that may have existed before.
I'd also like to point out there are no country on this green earth which claims Tibet other than China (ok, the ROC too). Hence it is not a "disputed" region by definition. Whereas J&K is disputed between two legitimate nation states (Pakistan and India).
THAT is a can of worms. You have to understand what imperial China was back then. It was a utter self-centered and complacent nation that thought there are no places worth living outside of China (or ZhongQuo, the middle kingdom).
What it did require of those heathens in the scrub lands was suzerainty. In return for token fealty and symbolic subservience, it granted generous gifts and if you didn't give it, you can expect an army at your door step to F' thing up. So while China and its emperors could care less about actually running those places and gave it great autonomy, it did consider it to be a part of its control area.
(Just as a side note, this is similar to the treatment that Vietnam recieve over history. IMO Vietnamese are kinda justified in hating China)
So when the Qing dynasty collapsed, and China fragment into De Facto warlord kingdoms, central control was lost, only to be re-establish by the communists in the 50's. Rule since then have been different in that for the first time direct China rule was administered, first through a puppet Dalai Lama, then nakedly by the CCP.