Native indians are indeginous to North America but not the American citizens of today! The same applies to South America! Black people are indeginous to Africa but not the white citizens of South Africa. Because those people had not originated from there, they arrived in boats after few other civilistions had existed in those places!
Using your theory the "Native Indians" are not native either because all human beings originate from Africa.
But that is not the case. They are native, because they were the people naturally inhabiting America when the whites came and took their land by force. Reminds you of anything?
The same goes for Cyprus. Greek Cypriots (not Greeks) which are the result of the assimilation between Cypriots, Greeks and other people, are the native people of Cyprus. TCs could also be part of the native people if they show that they are Cypriots, not just in terms of current location, but in terms of origin as well.
However Murataga rejects this connection and claims that Turks who came to Cyprus during the Ottoman rule did not mix with Cypriots. If we accept what Murataga says then TCs can not have any kind of connection with the natives of this island.