A theoretical investigation of the dynamics in a photoluminescence experiment in strong-coupling semiconductor microcavities is presented. Radiative recombination rates of microcavity polaritons in the strong-coupling regime and their scattering rates with acoustic phonons are used to study the polariton dynamics in a photoluminescence experiment, as a function of the temperature and the cavity detuning. It is found that the leaky modes of the distributed Bragg reflectors enclosing the cavity constitute the main sink of radiation, and that these modes dominate the whole recombination process. As a result, the rise and decay times are almost independent of the cavity detuning. Moreover, these times are close to those of the bare exciton at any temperature, thus showing little cavity influence on the overall photoluminescence dynamics.