The response time for a device is usually taken as the time to fully develop its signal. The time it takes for a photon to traverse a crystal is a fraction of a nanosecond. However the time it takes for the energy deposited in the crystal to manifest itself as a light pulse is substantially longer and is related to decay times of the types of crystal excitations. These excitation decay times can be fast i.e., 10-8 sec for luminescence or slow for phosphorescence 10-6 sec or longer. For solid scintillators it is a mixture.
You stated you are working on a simulation for a scintillation detector which includes a crystal and a photomulitpier tube. Depending the PMT used it could have a significant affect on the total response time of the detector.