In short, those who stayed in east, at historically sparsely populated steppes, remained more Asiatic, while those wo went to west came to lands with dense sedentary population, those people are not cleansed, many are intermarried with newcomers, some assimilated in groups. Its not just Turks of Turkey btw, Uzbeks, Turkmens, Uyghurs, Tatars etc. also have significiant amount of foreign genes in them.
Also not everyone you see from Turkey are Turks, Anatolia was always multi ethnic and still so, but many actual ethnic Turks still have Asiatic features.