Time-resolved photon counting technique was employed to study dynamics of photoluminescence from the ensemble and single CdSe/ZnS quantum dots with the alloyed core/shell interfaces. The ensemble data revealed enhanced effect of disorder-induced trap states for increasing emission energy, as implied from the changes in the distribution of total decay rates. The emission trajectories collected for single quantum dots showed familiar, two-state blinking pattern. It suggests that in a large-band-offset CdSe/ZnS system, the introduced alloying of the core-to-shell region cannot smooth enough the confinement potential in order to suppress nonradiative Auger recombination and blinking.