This paper proposes a strategy to manage an electric vehicle charging station (EVCSs) with a grid-side interface based on a Modular Multilevel Converter (MMC). In such a system, heterogeneous behavior of electric vehicles (EVs), that is independent arrivals-departures and different load demands, could lead to significant loading unbalances among the MMC arms and among the modules of a single arm. Nevertheless, the current in the grid interface must be kept balanced and sinusoidal. Furthermore, the voltages of the modules of an arm must be balanced. This work combines a load management (LM) strategy with a power flow management (PFM) algorithm to achieve the required characteristics of grid current and module voltages despite the internal unbalances of an MMC-based EVCSs. The LM optimizes the charging schedules and allocations of incoming EVs into charging units in order to minimize phase-to-phase and arm-to-arm unbalances in the system. The PFM algorithm controls the circulating currents to compensate the phase-to-phase, arm-to-arm and intra-arm unbalances of the given loading, which is determined by the LM strategy. The performance of the proposed optimal LM is compared with a benchmark LM that controls the system load without optimizing charging schedules and allocations of the EVs by simulating the daily operation of an example shopping mall parking with MMC-based grid interface. The results show how the optimal LM decreases the phase-to-phase and arm-to-arm unbalances. In scenarios with pronounced unbalance limitations, optimal LM increases supplied energy significantly. Real-time (RT) simulations are performed to observe grid current and module voltage profiles of the daily scenario in high resolution. The results demonstrate a balanced and sinusoidal grid current profile and balanced module voltages in MMC arms, and indicate that the proposed strategy combining LM and PFM is applicable for real-world deployments.