Following the observation of coherent oscillations in nonlinear spectra of photosynthetic pigment protein complexes, in particular, phycobilliproteins such as PC645, coherent vibronic transport has been suggested as a design principle for novel light-harvesting materials. Vibronic transport between energetically remote pigments is coherent when the presence of a vibration resonant with the electronic energy gap supports transient delocalization between the electronic excited states. We establish the mechanism of vibronic transport for a model heterodimer across a wide range of molecular parameter values. The resulting mechanistic map demonstrates that the molecular parameters of phycobiliproteins in fact support incoherent vibronic transport. This result points to an important design principle: Incoherent vibronic transport is more efficient than a coherent mechanism when energetic disorder exceeds the coupling between the donor and vibrationally excited acceptor states. Finally, our results suggest that the role of coherent vibronic transport in pigment protein complexes should be reevaluated.