Personally, I never pull from the center of the handle. I pull from exactly where I'll pull when shooting the bow. I WANT to see it tip if that's what it wants to do. Tipping at the very beginning of the draw is simply due, usually, to geometry. Meaning, since you're pulling the string from above the bow's center, it is going to want to tip to one side.... namely, since we're pulling from above center, the top limb will want to tip back toward the string. The degree of this depends on design... how far bow center is from the string fulcrum. The farther apart they are, more the bow wants to tip as the first bit of tension is applied to the string.
This is one of the main reasons I build my bows asymmetrically... it brings the bow center and string hand fulcrums considerably closer together.... so that less of this imbalance needs dealt with during tillering, timing, and shooting.