The dynamics of charging and recombination of photoexcited, site-controlled semiconductor quantum dots (QDs) are investigated using microphotoluminescence (PL) and photon-correlation spectroscopy combined with rate equation modeling. Several species of neutral and charged exciton complexes are identified in the PL spectra and their dynamics are evaluated by analyzing the temporal profiles of the second-order auto- and cross-correlation functions. The results provide insight into exciton dynamics relevant for designing QD structures for applications in quantum information processing and quantum communication systems.