Controlling polymer droplets remains challenging due to their complex non-Newtonian properties, especially elastoviscoplastic behavior, which combines yield stress and elastic responses. This study investigates the dynamics of elastoviscoplastic polymer droplet formation in flow-focused microchannels under active pulsatile flow regulation, by means of three-dimensional direct numerical simulations. The Saramito model is employed to describe the realistic polymer rheology, while the volume-of-fluid method, integrated with an adaptive mesh refinement algorithm, captures the droplet interface. As well verified by experiments, our results show that velocity pulsations enhance polymer droplet formation compared to constant flow rates. The flow regimes vary with pulsation frequency and amplitude, transitioning between thread, slug, drip, and jet flow patterns. Furthermore, a self-similar breakup behavior is observed during the pinch-off stage. The appropriate pulsatile flow frequency synchronizes the polymer droplet formation frequency, allowing precise control over droplet size and production rates. In the synchronization region, the droplet formation frequency aligns with the pulsation frequency, ranging from 75 Hz to 200 Hz, enabling droplet sizes to be controlled across a range with a variability of up to 2.7 times. Meanwhile, droplets of varying sizes can be produced on demand at a fixed formation frequency by altering the dispersed phase flow velocity. Finally, a semi-empirical model is proposed for predicting droplet size, incorporating pulsation parameters. These findings provide a basis for achieving on-demand control of polymer droplet production.