First, if you have lift cores made up of shear walls, these take most of the horizontal load, so the column moments arise mostly from deformation compatibility with the slabs and beams, mostly for vertical loads.
Second, larger moments may arise in some top columns near the shear walls due to axial shortening of the columns, which is larger in these elements due to the larger column stresses when compared to the ones in the walls. This effect may be overestimated as the axial deflection is being compensated during construction, so you may want to increase the axial stiffness of the columns to compensate a bit (do some hand calcs first to calibrate the axial stiffness increase) or do a full staged construction analysis with creep and shrinkage effects.
Hope it helps.