Efficient interfacial light-electric interconversion in van der Waals (vdW) heterostructures is crucial for their optoelectronic applications. However, an in-depth understanding of the necessary process for device operation, namely interfacial charge transfer (CT), has thus far remained elusive. In this study, by using photon energy-dependent transient THz spectroscopy, we complementarily investigate the interfacial CT process in heterostructures comprising monolayers of WSe2 and graphene with varying stacking orders on a sapphire substrate. We observe that the CT mechanism of the sub-A-exciton excitation is different from that of the above-A-exciton excitation. Notably, the CT process occurs via a photo-thermionic emission for sub-A-exciton excitations and a direct electron (or hole) transfer for above-A-exciton excitations. Furthermore, we demonstrate that the effective electric field induced by the sapphire substrate could adjust the Schottky barrier from a p-type contact (WSe2/Gr/sapphire) to an n-type contact (Gr/WSe2/sapphire). Consequently, it is more beneficial for the photo-thermionic electrons to transfer from graphene to WSe2 over the Schottky barrier in Gr/WSe2/sapphire. These results can provide new insights into the CT process in graphene-transition metal dichalcogenide (TMDC) vdW interfaces, which are critical to potential optoelectronic applications of graphene-TMDC heterostructures.