"If I adjust the nock height on a bow for me, will it be right for everyone that uses that bow?" No, not for everyone. Only for those who apply pressure to the bow and string the same way that you do. It's a matter of degree... so the farther they vary from 'your way' of shooting, the farther they'll move away from a well tuned bow.
"If so is there something about the bow that determines what the nock height should be?" Yes, kind of.... there are several factors that are inextricably connected/related that together determine a bow's dynamic balance, or imbalance. The bow hand fulcrum, the string hand fulcrum(largely determined by nock point location), the strength of each limb, even static balance and some other design basics. A change in any one of them can affect one or more others and the resulting dynamic balance. All linked, all relative.
The nock point is the easiest thing to adjust after the bow is finished, so that's probably why it's been given more credence than the other factors by archers... which carries over to bow making because it's those archer's that become bowyers. But bowyers would do well to think of it a little differently, and not think of the nock point location separate from those others, as an afterthought, merely as an adjustment, or 'fix'. If you have to move your nock point around in a search for good arrow flight, there's a very, very good chance the tiller isn't best for you. I put the nock point exactly where I designed it to be, to elevate the nock end of the arrow on all bows by 1/8", and then balance the bow relative to my fulcrums, throughout the tillering process, to shooting... and expect perfect arrow flight right where I put it from the first arrow shot(unless there's an arrow spine issue). It's very rare that I have to move it afterwards... in fact I don't remember the last time. Some folks build bows backwards, imo. Reverse engineering. Why?
To reiterate my point, and perhaps dig a little deeper into the "everyone that uses the bow" thing.... since nock point height affects where an archer's fingers are on the string(the string hand fulcrum), it directly affects dynamic balance. That balance or imbalance affects arrow flight, up and down, aka porpoising. Ok, that said....
The other fulcrum is the bow hand fulcrum, and even if a second archer grips the STRING exactly as you do, if he applies pressure differently to the handle, THAT fulcrum is moved, which also affects dynamic balance, and can cause a need for the tiller at brace to be changed, OR if the bow is done, for the nock point to be moved in an attempt to affect the relative limb strength in a good way.... or perhaps he could adjust his grip on the bow handle. All linked. All relative to balance.
