They are more like your ancestors of 15,000 years ago than you are. Think of them as the "original white people" but more adapted to sub-arctic climates.
Second, before the Turkish invasions from about the 900s to 1300s in the Middle East, most of the people in Anatolia (today's Turkish main homeland) were of Celtic, Greek or Semitic ancestry. The Celts and Greeks "moved in" during the First Millenium BCE, and this is talking about people all the way back to 10,000 BCE, so they'd be mostly descendants of folks who survived the last ice age in the Middle Eastern refugia ~ or the predecessors to those we call Semites today.
With respect to the Turks, their movement into Anatolia is comparatively modern, as you point out. But again, I was merely pointing to a Asian people who clearly moved in from Asia and decided to stay. This is an incredibly common phenomenon and I find is surprising that people think the populations were somehow static, and that the concept of agriculture was spread by word of mouth.
This whole thing sounds like a grant seeker stating something very obvious ("agriculture was spread by human migration") and pretending to disprove a notion that no one really held ("agriculture spread by word of mouth").