We show that Auger processes involving wetting layer transitions mediate emission from a cavity that is detuned from a quantum dot by even tens of meV. The wetting layer thus acts as a reservoir, which by Coulomb scattering can supply or absorb the energy difference between emitter and cavity. We perform microscopic calculations of the effect treating the wetting layer as a non-Markovian reservoir interacting with the coupled quantum dot-cavity system through Coulomb interactions. Experimentally, cavity feeding has been observed in the asymmetric detuning range of -10 to +45 meV. We show that this asymmetry arises naturally from the quasiequilibrium properties of the wetting layer reservoir. Furthermore, we present numerical calculations of both photoluminescence spectra and photon correlations, demonstrating good qualitative agreement with experiments.