The simulations and the results analyzed in this work clearly show that MTE is not adapted for these complex dynamics, while TSH-ED successfully captures the features of various time-dependent properties. Nonetheless, our adiabatic populations, especially for DMABN, show a different behavior if compared to the corresponding results obtained with the LVC models in Ref. [73], which highlights the fact that TSH-ED results might strongly depend on the parameters chosen for the simulations, such as the velocity rescaling, the decoherence correction, the treatment of frustrated hops.