Allot of tamils live in India. They are Indian citizens and are protected by the state.
The Tamils living in Sri Lanka are Sri Lankan citizens and are the responsibility of the Lankan government.
Tamils In India have a common heritage and culture with these people.
They offer them moral and political support.
This is very similar to the feelings Muslims in Pakistan have towards Muslims living in India.
The real problems arise when minorities are treated unfairly. This leads to resentment and sometimes it boils over into armed rebellion.
Asia has had its fair share of ethnic rebellions since the mid 20th century...
Tibetan rebellion against the PRC
Baluchi rebellion against Pakistan
Kashmiri rebellion against India
Bengali rebellion against Pakistan
Punjabi (Sikh) rebellion against India
Maoist rebellion against India
Tamil rebellion against Sri Lanka
Uighur rebellion against the PRC
and the list goes on.
They key to ending the tensions and violence is equal rights for all regardless of ethnicity, religion, caste, etc.
With equal rights and fair treatment within a society, the voices in the minority group calling for violence and independence become marginalized.
Lets hope the governments of the region can create more equitable and fair systems in order to end the turmoil in their respective countries.
Balkanization is not the answer.