We investigate the structure, topology, and dynamics of liquid water at the interface with natively hydroxylated (001) surfaces of InP and GaP photoelectrodes. Using ab initio molecular dynamics simulations, we show that contact with the semiconductor surface enhances the water hydrogen-bond strength at the interface. This leads to the formation of an ice-like structure, within which dynamically driven water dissociation and local proton hopping are amplified. Nevertheless, the structurally similar and isovalent InP and GaP surfaces generate qualitatively different interfacial water dynamics. This can be traced to slightly more covalent-like character in the binding of surface adsorbates to GaP, which results in a more rigid hydrogen-bond network that limits the explored topological phase space. As a consequence, local proton hopping can give rise to long-range surface proton transport on InP, whereas the process is kinetically limited on GaP. This allows for spatial separation of individual stages of hydrogen-evolving, multistep reactions on InP(001). Possible implications for the mechanisms of cathodic water splitting and photocorrosion on the two surfaces are considered in light of available experimental evidence.