Singlet exciton fission is the process in organic semiconductors through which a spin-singlet exciton converts into a pair of spin-triplet excitons residing on different chromophores, entangled in an overall spin-zero state. For some systems, singlet fission has been shown to occur on the 100 fs timescale and with a 200% yield, but the mechanism of this process remains uncertain. Here we study a model singlet fission system, TIPS-pentacene, using ultrafast vibronic spectroscopy. We observe that vibrational coherence in the initially photogenerated singlet state is transferred to the triplet state and show that this behaviour is effectively identical to that observed in ultrafast internal conversion for polyenes in solution. This similarity in vibronic dynamics suggest that both multi-molecular singlet fission and single-molecular internal conversion are mediated by the same underlying relaxation processes, based on strong coupling between nuclear and electronic degrees of freedom. In its most efficient form this leads to a conical intersection between the coupled electronic states.