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Tiller is not part of the bow rather it is the balance of a bow. It specifically refers to how the limbs bend, referring to the arc or curve and the tillering which is how they bend in relation to each other. Generally the upper limb, do to where the pivot point is in the grip area is slightly longer than the lower limb but they must still bend in equal arcs and with equal pressure. A tillering board which is easy to make is used to do the final tillering once the proper tapering has been done to the limbs.
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Wow, I don't know how long it would have taken for me to figure that out but you described it perfectly! I do recall a tillering thread showing a guy that drew a circle around a pic of him with the bow drawn - and the limbs fit the cirle amazingly.
You are the man ;)