Hybrid carbon materials are found to exhibit novel optoelectronic properties at their interfaces, but the related interfacial carrier dynamics is rarely explored theoretically. In this contribution, we have employed density functional theory (DFT) and DFT-based nonadiabatic dynamics methods to explore photoinduced interfacial electron transfer processes at interfaces between a single-walled carbon nanotube with chiral index (6,5) and C60 or C70 (C60@CNT65 and C70@CNT65). We have found that with low E11 excitation, electron transfer takes place from CNT65 to C60 and C70 in both heterojunctions. This process is ultrafast and completed within about 200 fs, which is consistent with recent experiments. Differently, high E22 excitation does not induce electron injection to C60 in C60@CNT65; instead, "hot" electrons produced within CNT65 will be trapped in its higher conduction band for a while because of slow inter-band relaxation. By contrast, in C70@CNT65, high E22 excitation still can lead to ultrafast electron transfer to C70, but only a comparable amount of electrons are transferred (ca. 30%). Interestingly, electrons either remaining on CNT65 or transferred to C70 are trapped in the higher conduction band for a while, similarly, due to slow inter-band relaxation. The present results could be useful to guide the design of excellent interfaces of mixed-dimensional hybrid carbon materials for various optoelectronic applications.