Supercapacitors are electricity storage systems with high power performances. Their short charge/discharge times are due to fast adsorption/desorption rates for the ions of the electrolyte on the electrode surface. Nanoporous carbon electrodes, which give larger capacitances than simpler geometries, might be expected to show poorer power performances because of the longer times taken by the ions to access the electrode interior. Experiments do not show such trends, however, and this remains to be explained at the molecular scale. Here we show that carbide-derived carbons exhibit heterogeneous and fast charging dynamics. We perform molecular dynamics simulations, with realistically modeled nanoporous electrodes and an ionic liquid electrolyte, in which the system, originally at equilibrium in the uncharged state, is suddenly perturbed by the application of an electric potential difference between the electrodes. The electrodes respond by charging progressively from the interface to the bulk as ions are exchanged between the nanopores and the electrolyte region. The simulation results are then injected into an equivalent circuit model, which allows us to calculate charging times for macroscopic-scale devices.