Buddhists who came from Tibet considers China have occupied their place, neither did these guys ever ask for Indian citizenship, When Dalai Lama goes to other place, he does it that way because to be an example indicating China have occupied their land and it rightfully belongs to them.
One cannot get a citizenship of a country and ask for a country from another country.
As an Indian we would be more than happy to have such people.
Next regarding Tamil Hindus of Srilanka, Many people from SriLanka live here in TamilNadu.
Nobody is denying them in India, They don't want to loose their land in SriLanka. If they come to India, they need to start from scratch, which is painful for anybody.