[eklavya]

That seems to be patently false. The oldest Tamil literature is Sangam literature (except Tolkāppiyam which is about grammar and contains influences from people all around India) which also contains poems for Vishnu, shiva, Durga. Buddhism and Jainism came way later.

[foolinaround]

AFAIK, Shiva is not mentioned at all in Sangam literature. The gods in both these cultures had similarities and a synthesis happened down the road.

for example, Murugan was the primary god and later assimilated with Shiva etc.