What must be considered is the fact that South Indians(not tamil) brought over by the Portuguese to work in Cinnamon fields near Colombo, disappeared into the Singhalese society. Why?? Because they were settled in Singhalese villages, they integrated and became Sinhale Buddhists within one generation.
That is why when the Dutch arrived, no tamil settlements were found anywhere in Lanka. The tamil's they brought over, were settled in East to work on fields but been fishermen, they moved to the coast. In the Ceylon History by Flavious 1816, you find a mention of these tamil's. Battecalao which today only has a Sinhala population 0.01%, in 1816 was 99%. The only school was a Sinhala school, the for mentioned Tamil's were settled and confined to islet of the mainland.
It was the British who learned from this and decided to settle tamil's in areas unpopulated, so that they would not integrate. Jaffna before 1833, had NO settled communities(Colbrooke Commission 1833). So the British choose to settle tamil's brought over for rail and road construction their but the east was well populated by hundreds of thousands of Sinhale. The British massacred most and by 1840, no people lived from Kandy to Trincomalee(Letter from Emerson Tennet to the Colonial office)!! It was then that, they started settling tamil's into the east.
It must also said that that the Portuguese, also have made recorded statements to the effect that their is NO agriculture in Jaffna. In other words, NO settled communities.
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Oldest humans remains found in Lanka, starting from 40000 years ago with Balangoda man shows that he is ancestor of the Sinhala and Veddha. This is an archeological fact.
The site of Pomparippu, in Mannar district. Which has a large collection of burials, dating 1000BCE onwards conclusively been shown DNA of Sinhala origin.
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Quotes
P.A.T. Gunasinghe says that Jaffna was populated by Singhalese in the medieval period as well. He says that the place names of Jaffna only make sense if they are seen as translations of Sinhala names. He points out that ‘vil’ means ‘bow,’ and ‘pay’ means ‘net’ in Tamil.
Therefore names like Kokuvil and Manipay only make sense when they are seen as the Tamilisation of the Sinhala words Kokavila and Mampe. Valikamam and Vimankam are meaningless in Tamil, but make sense if the villages originally bore the Sinhala names of Valigama and Vimangama. Some place names like Polvattai refer to the Sinhala used in 14th century.
Some random statements the book "Ancient Jaffna" by Mudaliyar C Rasanayagam"
*Page 384
"That Jaffna was occupied by the Singhalese earlier than by the Tamil's is seen not only in the place names of Jaffna, but also in some of the habits and customs of the people.
*Page v (Foreword)
" Dr. S. Krishnaswami Aiyangar of the Madras University writing on 29.8.1926 the Foreword to Ancient Jaffna by Mudaliyar C. Rasanayagam says: "The attempt of the author to derive the name Ilam does not appeal to us as quite successful; Ilam to us seems to be directly derived from the Pali word Sihalam, which in Tamil would be Singalam or even Singanam, but a strict Tamilising would make it Ilam...." Ancient Jaffna-Mudaliyar C Rasanayagam (Foreword p. v.).
*Page 382
" After the massacre of the Christians, Sankili's ( king of Jaffna) insane fury longed for more victims and he fell upon the Buddhists of Jaffna who were all Singhalese."
*Page 250
" Some others are of the opinion that 'Yalpanam' is the Tamil adaptation of the Singhalese name 'Yapane', which like many other Singhalese names of places in the district existed prior to the Tamil occupation......It is not at all surprising to see the name appearing in Sinhalese and Indian works earlier than in Tamil writings in Jaffna, for it appears that the application of the name for the whole district did not become popular among the inhabitants until the Portuguese period."
*Page 332
" Bhuvaneka Bahu (Kotte) who caused the Jaffna Town and the Nalur temple to be built was known as Sri Sanghabodhi, a title borne by the Singhalese kings....In the Kattiyam ( daily repeated at the Kandaswamy Temple) too he is referred to as Sri Sangabodhi Bhuvaneka Bahu."
"The account of the political divisions of Lanka sented by the schedule attached to Dharmapala's Donation must refer to a period long anterior to 1580, the date of the execution of this document, and so may find a place in this chapter. The states over which the king of Kotte claimed suzerainty were the kingdoms of Sitawaka, of the {Seven) Korales, of Candea or the hill-country, and of Jaffna, and also the principality of the Four Korales There also were various Vanniyarships, who were bound bo by tribute to the king of Kotte. These were the two Panamas; Yala; Wellewaya Kosgama; Wellassa; Palugama; Batticaloa; Kottiyar; Trincomalee: and Puttalam. This last and Yala were held by several Vanniyars, Palugama by two, the others by one each. In the kingdom of Kotte itself were three Disawas, one over Matara, one over the Adikariya of Denawaka with the Agras or gem-pits of Sabaragamuwa. and one over the Adikariya of Nuwarakalawiya, the country forming the western half of the present North Central Province and stretching according to our document from Puttalam to Mannar. Apart from this last Adikariya or jurisdiction, the immediate possessions of Kotte are given as 221 korales, which included the south-west corner of the North-Western Province, with a small exception the whole of the Western and Southern Provinces as far as the Walawe River, and that part of the Ratnapura District to the south of the Kalu-ganga with the great villages Gilimale and Bambarabotuwa. The small exception referred to is the half of Hewagam Korale, which belonged to Sitawaka. "