High penetration of electric vehicles (EVs) triggers challenges and opportunities for distribution system operators. Inverter-based EV chargers with active/reactive power control can be used to coordinate the EV fleet's charging process while providing local volt/var regulation. This paper proposes an adaptive robust programming model for the charging scheduling of EV fleets that exploits their capability to locally support the grid via reactive power control. The proposed model aims at maximizing the aggregator's revenue while considering the worst-case scenario in terms of active power losses at the supporting grid. Operational constraints of unbalanced three-phase distribution networks under demand uncertainty are also enforced. The proposed robust model is a min-max problem that can be linearized and solved using a column-and-constraint generation (CCG) method. Tests performed in a 25-node distribution system illustrate the EV fleet's capacity to support the grid while minimizing the total energy not supplied.