You are asking the right questions for the right reasons. These aspects of bow making are directly linked to how a bow carries, draws, shoots, how it treats the arrow and archer as a result, how easily it will be to tune, and whether or not it holds its tiller.
Here's one way to do it that I've found to work well for me... I generally design my bows so that the handle center is 3/4-7/8" below bow center. This makes the top limb 1 1/2 - 1 3/4" longer than the bottom, which allows it to balance in my hand the way I like, and keeps bow center, string fulcrum, and dynamic balance point all an inch or less from each other. This has several important benefits during and after tillering... but I digress.
The bow is placed on the tillering tree with its 4" handle centered and supported in a 4" cradle... which is level.
The string will be drawn from precisely where the center of my middle finger will be as I draw the bow, since this is my string hand fulcrum point. I find this exact spot on the wall behind my tillering tree by measuring over from the cradle(where the handle/shelf will be located) 3/8", which is where I set all of my nock points.... 3/8" above the shelf.... Then measure back from there the thickness of the arrow nock (1/4"), plus half the thickness of my middle finger (3/8"). So, this puts me at 1/4" in from the edge of the cradle (or down below the top of the handle/shelf). THIS is where I hook onto the string with my rope and pulley.... right where my middle finger will be with a 3/8" high nock point.
That point is also where I draw a vertical, plumb line on the wall for reference, from the cradle down toward the floor. This line represents the intended travel of the fulcrum point when limbs are balanced in strength relative to the string fulcrum. If they're not, the hook will drift toward the stronger acting limb as the bow is drawn, and it can be weakened as needed.
This adequately mimics how I shoot the bow, and I'm done tillering when I reach my draw length and the hook follows the line.
I give no regard to predetermined tiller measurements during the process. They are what they are when I'm done. This method balances limb strength in odd shaped bows, for example: one limb straight and the other reflexed, as well as it does those whose limbs look identical.