We address the problem of the photoluminescence of a quantum (QD) dot in a nanocavity, with focus on the case of nonzero detuning. In this regime, experiments have shown that strong emission from the cavity-like peak is still present for dot-cavity detuning exceeding 10 meV, which seems puzzling. We will discuss the general theory of cavity feeding, due to the relaxation and recombination kinetics of a multiply excited QD. We first compute the multi-exciton manifolds using a configuration-interaction scheme, starting from a truncated single-particle basis. We then run Monte-Carlo paths of excitation-emission kinetics on these states. This allows to extract photoluminescence spectra and two-photon correlation curves. The agreement with experimental data[1, 2] is very good. Our result shows unambiguously that the cavity feeding mechanism at large detunings can be attributed to excited-state multiexciton radiative decay (mostly biexcitons), also involving states in the wetting layer continuum.