To study further the factors and mechanisms controlling 10–150 keV particle fluxes in the inner magnetosphere, we investigate empirically their behavior in the nightside transition region (6–14 Re) depending on solar wind parameters taken at different time lags. We aim to establish the hierarchy of predictors (V, N, Pd, Ekl = VByz sin²(θ/2), etc.) and the optimal range of their time delays, both depending on the distance and local time. We use THEMIS 5-min averaged observations of energetic proton and electron fluxes in 2007–2018 near the plasma sheet midplane and build regression models exploring the combination of predictors, taken at time delays up to 24 h. The model obtained shows that protons and electrons are controlled differently by solar wind parameters: electrons are influenced equally by Vsw and Ekl, whereas protons are controlled mostly by Vsw and Pd and less by Ekl. We found that a wide range of time delays is involved depending on distance and particle energy. Specifically, the Ekl affects the energetic fluxes with time delays up to 24 h (or more), exhibiting the long delays in the innermost regions. As regards the mechanism of Vsw influence, the Vsw-related flux changes are large and, to a large extent, established on the route of the energy flow from solar wind to the plasma sheet and, eventually, the inner magnetosphere. We also identified a new parameter, NBL = VByz cos²(θ/2), which helps to reveal the loss processes in the plasma sheet transition region.