Hmmm...
Sounds like the only turks were dead turks.
So the peeps the swedes encountered before l4oo where what? Left over crusaders? franks? teutons? Vestigial carthaginians?
Or just plain old run of the mill greeks?
I'm not sure but I think later it was all Greek-speaking, although some of the Greek-speakers would have been descended from people who originally spoke another language.
I think it was held for a while by the Arabs and then regained by the Byzantines. The island was captured by Richard the Lion-heart during the Third Crusade (I don't know who held it just before that) but he soon sold the island to Guy de Lusignan. That family may have then held it until the Venetians acquired it. My guess is that the native population considered themselves "Romans" and were Greek Orthodox Christians speaking medieval Greek.