What you get from STAAD.Pro is the elastic deflection and you need to apply the Cd/Ie factor on top of it to get the design drift as outlined in ASCE. Now instead of multiplying the elastic displacement by Cd/Ie, it may be easier to divide the allowable drift factor by Cd/Ie so that the allowable drift computed that way can be directly compared to the elastic displacement coming from analysis.
Another point to note here is that, at any story level, STAAD.Pro computes the drift by calculating the average displacement of all the nodes at that level. If there is a rigid diaphragm defined, then the drift is calculated at the center of mass of the diaphragm.