The logic in the question is wrong, a Tamil poet mentioned about spherical shape of earth, so Tamil people invented that? The only true assumption you can be sure about from this poem is that Tamil people would have known about this fact 2000 years ago.
As Tamilnadu is a very small region in India there are chances that some others outside tamilnadu in India found this and the poet used the term long after it was invented. There are a lot of old languages in India. Tamil is one of them of course(as pointed out in the comments). But there are languages like Sanskrit which we need to consider. There are poems ,stories and puranas in that language too. Some of them are also mentioning about the spherical shape of earth.
For example, in Srimad Bhagavada(a holy book of Hindus), there is clear saying about the shape of earth. It is called 'BHUGOLA'(BHU means earth, GOLA means sphere in Sanskrit). There is a separate chapter for describing different planets including earth. This is surely older than the mentioned poem 'Thiruvasakam'. There are chances that Tamil people could have invented this, but the chances of other Indian people are also equal in finding this.
Also in Hindu puranas, the Earth is considered as the mother of humans and a goddess, and the people who wrote these puranas clearly knew that earth was spherical.
This google search shows result for the specific chapter about earth, see here
It's just an example, there are many other places where it is mentioned. Please keep in mind that these books are not specifically talking about the shape of the earth, it is used like a usual term in some places. They are not claiming anything about who invented things...
Also FYI, please have a look at these facts too which can not be found using the common sense.
Two thousand years before Pythagoras, philosophers in northern India had understood that gravitation held the solar system together, and that therefore the sun, the most massive object, had to be at its center.
Twenty-four centuries before Isaac Newton, the Hindu Rig-Veda asserted that gravitation held the universe together.
The Sanskrit speaking Aryans subscribed to the idea of a spherical earth in an era when the Greeks believed in a flat one. The Indians of the fifth century A.D. calculated the age of the earth as 4.3 billion years; scientists in 19th century England were convinced it was 100 million years. Many questions, still to be asked.
Read about the book Srimad Bhagavata, http://en.wikipedia.org/wiki/Bhagavata_Purana
For basic additional info about other assertions: http://en.wikiquote.org/wiki/Vedic_science and simple google search