Temporally varying turbulent flows are of considerable interest in complex engineering problems such as combustion, hydrodynamics, and hemodynamics. These types of flows are often associated with complex flow physics such as varying mean pressure gradients, interactions of different scales of motion, and complex boundary layer separations. Hybrid Reynolds-averaged Navier-Stokes (RANS)/Large-Eddy Simulation (LES) methods have recently shown promise for accurate and computationally efficient simulation of these flows. One such method is the dyanamic hybrid RANS-LES (DHRL) model which has been demonstrated for numerous statistically stationary turbulent flows. More recently, it has been shown that Exponential Time-Averaging (ETA) and Dynamic Time Filtering (DTF) methods for obtaining resolved flow statistics have significantly improved the predictive capabilities of the Dynamic Hybrid RANS-LES (DHRL) model performance for a non-stationary turbulent flows with periodically time-varying statistics. However, for non-periodic temporally evolving flows with monotonically varying statistics, a more suitable alternative is desired. In this study, the performance of the Dynamic Hybrid RANS-LES (DHRL) model with a double exponential dynamic time filtering (DDTF) methodology is evaluated against a Reynolds-Averaged Navier-Stokes (RANS) model, a conventional Hybrid RANS-LES (HRL) model, implicit LES, and the DHRL model with DTF for a pulsating channel and a temporally-varying turbulent mixing layer. Model performance is evaluated based on comparisons to existing experimental and Direct Numerical Simulation (DNS) results. A comprehensive analysis of the results highlights key similarities and differences between the models and indicates that the use of a double exponential DTF technique improves the accuracy of the baseline DHRL model. It is concluded that the DDTF is a useful alternative to simulate unsteady non-periodic temporally evolving turbulent flows.