The diffusion of salt ions and charged probe molecules in polyelectrolyte (PE) assemblies is often assumed to follow a theoretical hopping model, in which the diffusing ion hops between charged sites of chains based on electroneutrality. However, experimental verification of diffusing pathway at such microscales is difficult, and the corresponding molecular mechanisms remain elusive. In this study, we perform all-atom molecular dynamics simulations of salt diffusion in the PE assembly of poly(sodium-4-styrenesulfonate) (PSS) and poly-(diallyldimethylammonium chloride) (PDAC). Besides the ion hopping mode, the diffusing trajectories are found to present common features of a jump process, that is, subjecting to PE relaxation, water pockets in the structure open and close; thus, the ion can move from one pocket to another. Anomalous subdiffusion of ions and water is observed because of the trapping scenarios in these water pockets. The jump events are much rarer compared with ion hopping but significantly increases salt diffusion with increasing temperature. Our result strongly indicates that salt diffusion in hydrated PDAC/PSS is a combined process of ion hopping and jump motion. This provides a new molecular explanation for the coupling of salt motion with chain motion and the nonlinear increase of salt diffusion at glass-transition temperature.