BLA has been internationally recognized as a terrorist outfit for killing Baluch teachers, professors and intellectuals that believe Baluchistan's freedom cannot be attained and it's survival will be at risk post-Pakistan as another power will comfortably take over then (Iran is an example).
Therefore, you might need to reconsider your personal opinions regarding well-known terrorist groups.
Naam Taamilar has never been involved in terrorism and neither has it ever sympathized with them. You may want to watch the trailer to see the kind of abuse the Tamilians are being put under and how their dignity is being berated when the Persian Aryan John Abraham slaps one of them, barbarically.
Naam Tamilaar is that movement - the catalyst is the movie, as you've rightly pointed out - and, the methodology is the one seen in Egypt's Tahrir Square.
They have locked down Chennai on many occasions but doing so for a month and the entire parliament resigning indefinitely or passing the resolution to free Tamil Nadu like GM Syed did with Pakistan in Sindh, might achieve the dream all Tamilians, from Singapore to San Fransisco aspire for.
Imran Khan vs Pakistan: Protest of Treachery - Casualty Report