"We pull on the rope and the idea is that the hook should follow the plumb line right to full draw. Am I right so far?"
Yes, generally. Except, the farther apart your bow's center and string fulcrum, the harder time you'll have getting the hook to follow the line early in the draw, but you can still tiller it so it gets there. At full draw, they should all be balanced, or very nearly so... there may be reasons to leave this or that limb a hair stronger, dynamically. This is an additional reason I prefer asymmetrical bows, for myself, at least. The bow center and fulcrums are all closer to one another, within a fraction of an inch, or can even all be put in the exact same place in some cases(three under), and the bow draws in a very silky smooth clean straight line from beginning to end. Once you feel it, you'll likely not want it any other way.
"Lets say the hook travels to the left of the plumb line. What do we do to the tiller to correct that?"
Before I answer, I need to know whether your bow is being supported in the tree so it cannot tilt on the cradle, or if it is allowed to move freely. To start at least, because it's a better initial indicator, I like the handle to be perfectly level and supported so that it can't tilt. Get the handle section level. Don't worry about whether one tip is in front of the other. This mistake is often made.
When the handle is level and supported there, the hook will drift toward the stronger limb as the limbs are flexed when pulled from our string hand fulcrum. Even/also when long string tillering, it will go toward the stronger limb. That's why I like to use the long string on the tree instead of floor tillering. I get an early indication of dynamic limb balance, and begin making early adjustments, which I think ultimately helps retard set in the limbs. And by stronger limb, I don't mean how it 'looks' at brace, I mean stronger relative to the other limb and the string fulcrum. Stronger in how it acts... indicated by how the hook travels.
Weaken the limb that the hook drifts toward. That's the stronger limb.
DC, this is what I always liked about you. You're inquisitive and ask the questions I wish all would ask... not of me necessarily, I'm a busy guy... lol... of themselves... of their work, of their bows. Bows know and try desperately to convey to us what they need. 'Why does the bow tilt in the hand?' 'Why does the bottom limb always take more set?' 'Why do they all feel and shoot differently?' We should listen.
I'm telling you guys... you can build bows that are inherently tuned and shoot the same. You can just as easily, or more-so, craft them so that they'll shoot that first arrow perfectly, predictably... one bow after another, than you can while trying to move the nocking point or change your grip on the bow, or retiller it afterwards. Blech. Not me. This is simply building in a straightforward, predictable manner from the get-go to achieve what we all value in our bows, no guessing, no backtracking.
