Not a historian but there's an important confounder to this observation that you need to be aware of, regarding eye color:

After the age of about 55, and in even younger individuals with high cholesterol, there's a significant amount of cholesterol that gets deposited into the cornea (front window of the eye). This often gives the illusion that their eyes are turning blue, when in face their iris is unchanged. This is especially noticeable in people with darker eyes. I very often hear from older Black or Latino patients that their "eyes are turning blue."

Click here for an example.

Now, of course this doesn't address the skin tone question, and I'm sure doesn't account for all of your observations either. This is just something to be aware of when looking at the eye color difference.

Source: Me (optometrist).

(Hopefully this doesn't get deleted by the mods. Not my goal to provide an answer to the history question; merely to present a possible explanation for the observation.)

In general, Turks from the Balkans, the Aegean, and the Black Sea are more likely to have fair skin and light eyes. Turks from Central Anatolian and Southeastern Anatolia tend to have more olive skin and darker eyes. Of course, this is just probablistic and there's a huge range of phenotypes throught Turkey--while Kurds are stereotypically somewhat darker than other citizens of Turkey, but there are plenty of Kurds with red hair, pale skin, and fair eyes.

Families that are Turkish today were not necessarily Turkish two hundred years ago, never mind five hundred years ago. Every population study of Turks has found a large mix of Central Asian (the original Turkic homeland), Middle Eastern (through intermarriage with and cultural change of Arab, Persian, etc), and European (through intermarriage with and conversion of Greeks, Circassians, Albanians, and Balkan Slavs) origin haploid groups. I'm not sure where genetic studies of Armenians put them (to be honest, probably mix similar to Turks with less Central Asian), but there were massive amounts of mixture between Armenians and Turks/Kurds right up through 1918 (Turks with Armenian heritage have had a new historical awareness thanks to a series of books published in the last decade on the Armenian orphans of the violence of 1915-1918 who were adopted by Turkish families).

But these genotypes are probably regionally unequally distributed across the Turkish population because the phenotypes certainly are. I'm a fair eyed Ashkenazi Jew and I can pass for Turkish, but I only look like someone from the Aegean region, apparently. My best friend is American of Welsh-English-Dutch descent but in Turkey people assume he's from the Black Sea before he opens his mouth, because he has several features that Turks associate with the Black Sea: fine, straight hair, light eyes, pale skin, and above all a very wide nose. One of my friends is from Mersin and she explained that a lot of people in her town have the same darker skin and frizzy hair she has because a lot of Muslim refugees came to Mersin from Crete when the Greeks took over the island, and there were a lot of Black Muslims (former slaves) on Crete who married with the other Muslims of the island. One interesting thing is that while looking "Kurdish" can be detrimental, there's not the same skin tone hierarchy in Turkey that you find in, say, Latin America or India. Instead, there is a range of ways to look "Turkish", none better or more Turkish than the others. Similarly, there's a range of ways to look white in America. White people in New York and New Jersey may be more likely to have dark hair and Mediterreanian features than people in, say, Minnesota, because New York and New Jersey had a lot of Jewish and Italian immigration and Minnesota had a lot of Scandinavian migration.

So, if what you're seeing is a real phenomenon, it's likely that the Turkish migrants you're seeing came in different waves from different regions of Turkey. If you're interested, I think the Turkish statistical bureau keeps emigration records so you can see where people are migrating from in different periods, though I've only had to look up recent ones and don't know how far back the publicly available records go.

It would help if you shared more information about where the community is located and if you know anything about the members composing it. Are they from the Black Sea region? Are they from the east? And are you comparing the older generation to a younger generation from the same region? Eye color is determined genetically. You may just be making a generalization based on a small sample size.