That’s true; the Ancient Romans and Greeks ( Alexander ) went almost everywhere! But I doubt that they had hazel eyes coloring.
Well, my point is that eye color is genetic, and genes go where people do.
The video on hazel eyes seems to indicate that brown eyed and blue eyed people in the Iberian area seem to have first intermixed 8 to 6 thousand years ago; and that’s where the hazel eyes started. Then people moved around.