EV chargers can be controlled to support the grid frequency by implementing a standard-compliant fast Primary Frequency Control (PFC). This paper addresses potential effects on power systems due to control discreteness in aggregated electric vehicles (EVs) when providing frequency regulation. Possible consequences of a discrete response, as reserve provision error and induced grid frequency oscillations, are first identified by a theoretical analysis both for large power systems and for microgrids. Thus, an EV fleet management solution relying on shifting the droop characteristic for the individual EVs is proposed. The PFC is implemented in a microgrid with a Power-Hardware-in-the-Loop approach to complement the investigation with an experimental validation. Both the analytical and the experimental results demonstrate how the controller performance is influenced by the response granularity and that related oscillations can be prevented either by reducing the response granularity or by applying appropriate shifts on the droop characteristics for individual EVs.