What I learned in the class I took from Rod Jenkins was to not move my head at all when I draw the bow and shoot the arrow. My head should be in an upright position, turned toward the target, with my dominant eye located over the centerline of my body.
In that position, you should be able to draw the bow so the string actually bisects your eye, which means the arrow would be exactly under your eye. Your head should be turned enough that your nose should be out of the way to the side. Your anchor is on the side of your face, and not in front of your mouth.
Most of us don't want the string exactly in front of our eye, so we anchor a little more to the side or cant the bow a little, so maybe the string is visible in the corner of our eye, so the arrow may be slightly away from being right under the dominant eye. I understand that some people do learn to shoot with the string right in front of their eye.
Just what works for me, YMMV, of course.