Photons which are generated in a two-photon cascade process have an underlying time correlation since the spontaneous emission of the upper level populates the intermediate state. This correlation leads to a reduction of the purity of the photon emitted from the intermediate state. Here we characterize this time correlation for the biexciton-exciton cascade of an InAs/GaAs quantum dot.We show that the correlation can be reduced by tuning the biexciton transition in resonance to a planar distributed Bragg reflector cavity. The enhanced and inhibited emission into the cavity accelerates the biexciton emission and slows down the exciton emission thus reduces the correlation and increases the purity of the exciton photon. This is essential for schemes like creating time-bin entangled photon pairs from quantum dot systems.