It is actually a bit of a myth that everyone believed the world to be flat until Columbus. It is true that a lot of ancient societies believed that as a matter of cultural mythology. This was true both for the ancient Greeks as well as the ancient Indians.
However, any ancient navigator who looked to the horizon on the sea on a calm day could clearly see that it was curved, and that distant ships appeared to sink lower as they approached it. So educated men the world over eventually realized they were sitting on some kind of giant sphere from a very early time. That time seems to be sometime after about the 5th Century BC in the Greek world, and according you your poet at least as early as the writing of Tiruvacakam in the subcontinent (5th-7th century AD. one would imagine far earlier than that though, as there was regular seaborne trade going on in that area as early as the Roman era)
For example, some people incorrectly credit Erathostenes with the idea of a spherical earth, while what he really did was take that as a known given (which it was at the time) and tried to calculate its circumference.
So from a strict technical sense, yes you could say that the Tamil people probably knew the earth was round 2000 years ago. However, pretty much everyone else with access to a large body of water knew that too.