Type-II band alignment structure is coveted in the design of photovoltaic devices, since it is beneficial for the transport of photogenerated carriers. Here we study the generation and recombination dynamics of carriers in a type-II quantum structure composed of ZnSe0.92Te0.08 highly mismatched alloys (HMAs) and Zn0.97Mn0.03Se. The photoinduced holes at the ZnSe0.92Te0.08 HMAs firstly undergo rapid relaxation to the isoelectronic centers above the valence band edge and subsequently recombine with the free electrons in the Zn0.97Mn0.03Se. The long carrier lifetimes over 120 ns induced by spatially indirect excitons that are bound to isoelectronic Te trapping states further increase with increasing temperature.