"Does tiller affect nock height?"
The best placement for it? Absolutely. How could it not? The spot to place the arrow on the string for best flight and bow behavior is directly related to limb strength relative to one another and the archer's holds on the bow's handle and string.
Archers setting up a new bow(generically tillered) often have to move nock point location around to find the spot best suited to their particular shooting idioms... or adjust their form to suit the bow. If the bow isn't designed or tillered to suit them very well, they may have to move it far to bring things into some semblence of balance and decent arrow flight.
As bowyers however, we have an advantage in that we can predict where we want to nock the arrow, and then design
and tiller the bow so that it balances at full draw and shoots an arrow perfectly straight away from that spot relative to the archer's holds I mentioned. It likely sounds more complicated than it is, but actually in my experience, it makes design, construction, tillering, and tuning more cut and dry, predictable, with no guesswork or backtracking. I know exactly where I'm going to set my nock point before I even pick up a stave to begin, and I know that when its done, it will be perfectly balanced when I draw it from there and won't need to be moved.
By the way, I place the arrow under the nock point and set the nock point 3/8" above the shelf... this gives the tail end of the arrow about 1/8" elevation above the shelf as it passes.