The interaction between wakes and rotors is typically detrimental in terms of the overall power production of a wind farm. The recently studied wind farm controllers represent a promising way to increase the energy harvested through the mitigation of the effects induced by wake impingement. Recently, a novel methodology, based on a dynamic variation of induction, has been proposed as an alternative to steady induction and wake redirection controls. According to this new technology, a periodic collective motion of blade pitch generates a dynamic induction, associated with a stronger flow mixing and therefore a faster wake recovery. Although this technique proved to be effective in terms of power increase, both in numerical simulations and in wind tunnel experiments, much is to be done in order to demonstrate its feasibility. In particular, the impact of dynamic induction control in terms of downstream turbine dynamics has not been yet analyzed in detail. This paper presents a CFD-based analysis aimed at describing the response of a downstream rotor inside the wake of an upstream machine performing dynamic induction control. Specifically, the periodic induction entails a pulsating flow downstream which interacts significantly with the aero-servo-elastic dynamics of the downstream turbines. For low wind speeds, such an oscillating flow may trigger a shut-down/start-up sequence any time the velocity results lower than the cut-in speed.