Optically detected single-turnover measurements of biological and inorganic catalysts provide a detailed picture of structural and dynamical influences on catalytic activity. Measurement at the single-molecule level of catalysis of a fluorogenic reaction (or its reverse) yields a stochastic fluorescence trajectory reflecting the statistics of individual reaction and product dissociation events. Analysis of time correlations displayed by this trajectory reveals reaction details inaccessible in a bulk measurement of averaged dynamics. Superresolution optical detection techniques can provide a spatial resolution over which correlations could be observed in space as well as time. A model is constructed here for spatial correlations in catalytic activity produced by an entity transported among multiple active sites. An approximation strategy based on perturbation theory in the coupling between transport and reaction dynamics is applied to calculate the mean dwell time of a reactant on an active site and the correlation between dwell times of reactants at different locations.