Evidence suggests that it was the Brahmins who had the most pronounced influence in Southeast Asian culture due to the the fact that languages there are heavily influenced by Sanskrit, not Tamil. As such, Hindu epics, like the Ramayana and Mahabharata, became quite popular in Southeast Asia, including Indonesia, as seen by the presence of a statue of the Gitopadesh scene in the Mahabharata in the Indonesian capital. In addition, Dravidian temple architecture became quite ubiquitous in these parts, even though Dravidian linguistic influence from Tamil was minimal. This is due to the fact that while the Chola Empire governed a predominantly Tamil speaking region in India, it was Brahmins trained in Sanskritic knowledge who traveled to Southeast Asia. The so-called Indianization of Southeast Asia has had a very large influence on the culture there, as can be seen from the fact that Hindu epics and culture are still very popular in Indonesia even as the country has a majority Muslim population. In later centuries, Islam too arrived in Indonesia from India, but this was not during the rule of the Chola Empire.

Sources: IW Mabbet, “Indianization of Southeast Asia”, Upinder Singh, “History of the Chola Empire”