We explore the correlated dynamics of an electron hole and a proton after ionization of a protonated water cluster by extreme ultraviolet light. An ultrafast decay mechanism is found in which the proton-hole dynamics after the ionization are driven by electrostatic repulsion and involve a strong coupling between the nuclear and electronic degrees of freedom. We describe the system by a quantum-dynamical approach and show that nonadiabatic effects are a key element of the mechanism by which electron and proton repel each other and become localized at opposite sides of the cluster. Based on the generality of the decay mechanism, similar effects may be expected for other ionized systems featuring hydrogen bonds.