There is no evidence that Tamils existed as a significant, distinct single nation in Sri Lanka prior to the 13th century. There was never a single nation called "Tamil" anyway. There is a language, but those who spoke it were identified by lineages/dynasties such as Pandya and Chola, or simply as "Tamilar" based on the language spoken. That is why massive caste divisions still persist today. Under the Tamil Eelam myth, Tamils in the northern part of Sri Lanka claim this as their homeland. Europeans referred to the northern Tamils as "Malabars." Back then, Europeans brought people to do their work from the Malabar coast and areas known as the Coromandel Coast. The people there were generally referred to as Malabars. Even before that, under a South Indian Tamil ruler named Sankili, mercenaries from Andhra (Telugu), Kannada (Karnataka), Malayali (Kerala), and Tamil Nadu all arrived in Jaffna. Earlier still, Kerala soldiers brought by Kalinga Magha moved to the north when Magha was defeated and fled. Because of this, the Kerala population became a majority in the north over time. Furthermore, due to Sankili's rule, the Sinhalese people living in the north were expelled, and those who remained mixed with the incoming populations. That is why Jaffna Tamils have Tamil names that do not even exist in Tamil Nadu. Even the caste system in Jaffna is different from Tamil Nadu; it is somewhat similar to the caste system in Kerala. Jaffna Tamil is also close to Malayalam.
The estate Tamil group, although considered lower-caste, is an actual group from Tamil Nadu—they are the authentic Tamils. Those from Jaffna are like a mixture (kottu), yet they claim they are the real ones who speak "pure Tamil." It was only in the 19th century that they approached the British to label them as "Sri Lankan Tamils" and manufactured an identity to advance their interests. Until then, they were called Malabars, which included all those ethnicities mentioned above. In addition, during the colonial period, the Portuguese and the Dutch brought Malabars from the Malabar coast and granted them land under Dutch rule. Malayalam became a completely independent language only around the 13th century; until then, they all spoke essentially the same language. Therefore, their language retains elements of Old Tamil. The majority who came here for migrations, invasions, and slave labor before Malayalam became an independent language were from Kerala. Because of this, they portray themselves to the world as "pure Tamil," whereas the majority are people of Kerala origins hiding behind a Tamil Nadu identity.
Furthermore, their own Yalpana Vaipava Malai—a later text filled with myths regarding Tamil Eelam—mentions the expulsion of Sinhalese people from Jaffna and how settlements were established. The Vallipuram gold plate confirms that in the 2nd century CE, Jaffna was governed by a Sinhalese minister named Isigiri. Tamils in Tamil Nadu do not understand these nuances, yet they trust these Jaffna Tamils in their quest for a separate state. The Jaffna group is extremely cunning; they incite people in Tamil Nadu by talking about Eelam, but when Tamil Nadu fishermen poach fisheries resources in northern waters, they mockingly ask the Sinhalese whether the government is afraid of India. The Jaffna Malabars act as such double agents.
The composition of the Malabars = Kerala culture + Old Tamil language + arrival from that region before its people fully differentiated into Malayalis + claiming to be "pure Tamils" speaking "pure Tamil" by capitalizing on that Old Tamil usage + mixed Sinhalese genes contributing to a fairer, Sinhalese-like appearance. Among the Tamils here, the estate Tamils are naive and lack awareness about these complexities; the Jaffna Tamils marginalize them as lower-caste, yet despite being marginalized, they still support Fake Tamil Eelam.
And mostly it is christians like you spread this misinformation that there was a genocide.