The phonon-assisted recombination in bulk II-VI semi-conductors is analyzed by means of time-resolved photoluminescence spectroscopy. Experimental results on both CdS and CdSe clearly indicate that phonon-sideband emission is not exclusively attributed to the presence of excitons. The contributions of Coulombcorrelated electron-hole plasma to the phonon assisted recombination may be significant, depending on the excitation conditions. This observation is supported by a microscopic many-particle theory of interacting electrons, phonons, and photons. Our theoretical approach generalizes previous investigations by including both correlated and uncorrelated luminescence sources. Our findings contradict and expand the traditional picture of phonon-sideband emission.