Tamils, Telugus and Kannadigas celebrate Deepaavali (not Diwali). Meanwhile Kerala in the south does not celebrate Deepaavali. In Kerala, King Bali's death is associated with this day. The stories behind the Deepaavali in the south and Diwali in the north are different. In the south it is not about Rama returning to Ayodhya, but it is about some Asura (demon) called Narakasura being killed by Krishna or Kali (Sakthi).
Some 30 years ago or so only a small fraction of Tamils, say like 10-15% of the people, celebrated, even in a big city like Chennai (then called Madras). The number of people who are celebrating it has now increased, but even today, in spite of its popularity, it is not the majority of the people who celebrate it and they don't really connect or identify really.
The difference in the date may be because they signify different stories. The Diwali in South India is considered as a victory of Lord Krishna of the demon Naraka on the day of chaturdasi. During his death Naraka requested that people celebrate the victory of good over evil with new clothes, bursting of crackers etc. People in Tamilnadu do not consider Diwali as festival as lights as we have a separate one during the Kartik Month according to Tamil Calendar.
