RE: tuning question
If the arrows are flying "true", meaning straight, then they should not impact nock left or right. Once they are flying straight, a sight adjustment should be all that's needed.
But, a bow can be adjusted to centershot using the walk-back method, and arrow flight can still be poor for reasons unrelated to centershot. Obvious reasons are form, arrow spine, arrow/fletch contact with cables orthe rest, etc. There are probably others too, and I know I don't understand them all.
I know that occasionally I'll torque the grip and see a fish-tail.
I have no idea what the target material is, but if it has some grain to it, it may grab the arrow and make it seem like they are not flying straight.