In high Mach number turbulent reactive flows, spontaneous ignition appears as a key ingredient for the stabilization of combustion. In our previous analyses devoted to such conditions, chemical kinetics as well as associated finite rate chemistry effects have already received considerable attention. However, the representation of flow time scales, such as residence and mixing time scales, still requires further work. The present modeling study is devoted to this peculiar point. Hence, a transport equation for the quantity of residence time is considered to evaluate the mean residence time associated with both oxidizer and fuel injection streams, while a modeled transport equation for the mean scalar dissipation rate (SDR) is considered to estimate the scalar mixing time scale. This allows us to improve the description of turbulent mixing, including the large-scale engulfment processes through the consideration of the residence time scale, as well as the small-scale molecular mixing processes, the intensity of which is set by the integral scalar (mixing) time scale. Some insights are gained from the analysis of the evolution of the different production terms that appear in the mean SDR transport equation. The model capabilities are evaluated through a comparison between numerical results and the data obtained from experimental studies devoted to supersonic coflowing jets of hydrogen and vitiated air. The first simulated test case corresponds to a detailed experimental database that includes Raman scaterring and laser-induced pre-dissociative fluorescence measurements. Albeit less documented, the second test case is retained to confirm the relevance of the proposed closure. Finally, the comparisons performed with the two distinct sets of experimental data establish that the main physical processes are well-described by the proposed approach.