We show, by time-resolved magneto-photoluminescence (PL) spectroscopy in combination with selective laser excitation, that optical polarization of the ZnCdSe spin detector induced by spin injection from the ZnMnSe spin injector persists over a much longer time scale than the lifetime of the ZnMnSe excitons. This finding provides compelling experimental evidence that the dominant mechanism for the observed spin injection in the ZnMnSe/ZnCdSe structures should not be due to injection of the excitonic spins of the diluted magnetic semiconductor (DMS). It is rather due to e.g. a delayed spin injection arising from tunneling of individual carriers or/and trapped spins in ZnMnSe.