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He is trying to center the bore but it is not concentric with od.
I don't have a lot of lathe experience I like mill work better.
I will ask about what jaws he is using I imagine 3 jaw .
The bore should be dialed to the center line of your lathe to less than .001" . Ideally it should be less than .0005". If you're new to chambering than it can take some time and patience.
Concentricity of the outer contour to the lathe center line is not really important, although most gunsmith's will clock the barrel so the high point is in the 12 o'clock position.
The bore of most barrels will not run concentric to the outer contour along it's entire path.
If you're measuring .01" and .006" from the bore of your barrel you need to spend some extra time dialing things in.