The objective of this work is to apply a model that accounts for the presence of shallow traps to the analysis of pulsed optically stimulated luminescence (POSL) data, which is used to characterize the luminescence lifetime and thermal quenching of luminescent materials. In particular, we focus on the analysis of photon arrival time distribution (PATD) data obtained by POSL readouts of irradiated materials. To achieve this, we present the detailed analysis of a PATD experiment over a range of readout temperatures of a well-known dosimetric material, Al₂O₃:C. Hitherto, an exact model accounting for the previously observed luminescence lifetime over-estimation is missing. Herein, we apply a proposed model that accounts for the influence of shallow traps and show how this model corrects for the luminescence lifetime over-estimation and introduces the temperature-dependent shallow trap lifetime as a new parameter. We furthermore show that populated deep electron traps lead to a stronger shallow trap occupation, which could be quantified with our model. The results are relevant for both the interpretation of thermal quenching models of Al₂O₃:C and, more generally, for lifetime measurements in luminescent materials.