The growing uptake of electric vehicles (EVs) will likely require management schemes to enable their connection into distribution systems. While most of the existing approaches are developed from the operator's perspective considering EV aggregated demands at the medium-voltage (MV) level, individual users' comfort and the particularities associated with low-voltage (LV) networks need to be considered to holistically assess the EV effects in an integrated MV/LV network. This article proposes a two-level hierarchical optimization framework for the EV charging coordination (EVCC) that maximizes users' satisfaction, while avoiding operational grid issues in the whole distribution system. The framework is tailored for unbalanced distribution systems with high penetration of EVs and introduces a novel index to measure charging priority-based EV user satisfaction. To reduce the computational burden, the EVCC problem is disaggregated into an upper level for MV network operation, and a lower level for LV network and individual EV scheduling, using mixed-integer linear programming models. This framework is later embedded in a dynamic scheduling approach that copes with unexpected EV arrivals. Benefits (increased overall user satisfaction and reduced strain over distribution assets) are demonstrated via case studies in a 459-node three-phase network in which solutions were achieved under a 60-s threshold.