We now study a case where the effect of the transient difference between NE-FGR and E-FGR results in a more prominent difference in the dynamics. To this end, we consider the case where the lower polariton is initially populated, such that the short-time dynamics are dominated by energetically unfavorable k -→D where the transient rate from NE-FGR is significantly larger than its equilibrium limit E-FGR rate. The resulting population dynamics are showcased in Fig. . Since the upper polariton never receives any significant population (P + ≈ 0), Fig. only presents the dark state population for comparison (whereas the P -≈ 1 -P D ). Not surprisingly, the E-FGR underestimates the dark state population in all three cases of light-matter detunings, since the E-FGR rate constant lacks the transient spike in k -→D (t) (see panel (d) in Figs. ). The deviation between NE-FGR and its time-nonlocal counterpart TNL is not significant, since the relatively slow |-⟩ → |D⟩ process makes P j (t) = P j (t -s) a valid approximation (comparing Eq. 11 to Eq. 16a). Further comparing to the exact HEOM result reveals that the NE-FGR and TNL give very accurate dynamics. This means that NE-FGR captures some important non-Markovian nature of the dynamics. The E-FGR dynamics, on the other hand, has a substantial difference compared to the NE-FGR and HEOM dynamics, indicating that E-FGR and a simple rate equation is not adequate to capture the dynamics and the full time-dependent NE-FGR rate expression is necessary for this case. This importance of using NE-FGR in the transient timescale is likely to be general for population dynamics starting from LP, since in the collective regime, the dynamics would be dominated by k -→D which does not scale unfavorably with 1/N .