It might be oversimplifying, but with a hunting bow, you do not want to be under spined...or close to under spined. I know, I know- some pros tell us under spined is more forgiving. It's one of the rare cases I disagree with those pros. Those guys mostly shoot FP's and low pro short mech heads.
Consider; those pros are like machines; exact and consistent every time. A noodle arrow works in that case. But then put a BH on there that can plane out of the bow if its not perfectly aligned...or a hunt scenario where you might have less than perfect form and IMO, you want the stiffer arrow thats less likely to noodle in a different way.
I have always shot a spine size over...or slightly stiff and never had a bow that wouldn't shoot fixed BH's to the same POA as my FP's at 50y.
I can push arrows to the side by increasing face pressure- so yeah, it's a thing. You want to be anchored in the same place but no need to pull hard into your face vs straight back.
Cam Timing, it's when the cams roll over at the exact same time. Some bows shoot a little better with the top cam hitting the stop 1/16 early, or vice versa.
Shops can do it but I would offer to pay them for their time- which could take longer than you think. I have all of the stuff at home.
The good news is once you know the tuning process- it's much easier after that.
Yours could be as simple as you might have been moving the rest too much at one time.