Mike, you said when you pull the string, the top limb tilts down... If it does so sharply, that sounds like what happens when a symmetrically made bow is 'properly' drawn on a tree because the string is pulled far above center(its static balance point). Ultimately, if we balance the limbs well enough, it will drift closer to the line the farther it's drawn and somewhere prior to full draw, it should be right on the line... i.e. dynamically balanced at full draw... if we do our part balancing the limbs by wood removal.
What you are seeing is the beginning of 'the shift' between static and dynamic balances that happens when many bows are drawn. Even asymmetrical bows will do it to a lesser degree if the longitudinal center and string fulcrums are separated.(as mine often are). I find this shift, if bad enough, can negatively affect how a bow feels during the draw and release, and even think it affects arrow flight and tuning ease/difficulty. Its severity depends on location of longitudinal center relative to string hand fulcrum, and can be greatly reduced, even virtually eliminated by designing these factors in close proximity to one another, or even at the exact same spot in some instances.... and these, if the limbs are in fact balanced relative to the archer's holds, make the most predictable, inherently tuned, sweetest drawing and shooting bows, imho.
Does your bow have same length limbs, or a shorter bottom? Do you shoot split finger, three under, or?