We examine the role of surface passivation on carrier trapping and nonlinear recombination dynamics in hybrid metal-halide perovskites by means of excitation correlation photoluminescence (ECPL) spectroscopy. We find that carrier trapping occurs on subnanosecond timescales in both control (unpassivated) and passivated samples, which is consistent within a shallow-trap model. However, the impact of passivation has a direct effect on both shallow and deep traps. Our results reveal that the effect of passivation of deep traps is responsible for the increase of the carrier lifetimes, while the passivation of shallow traps reduces the excitation density required for shallow-trap saturation. Our work demonstrates how ECPL provides details about the passivation of shallow traps beyond those available via conventional time-resolved photoluminescence techniques.