The chemical-diffusion and surface-exchange coefficients of a proton-conducting oxide, i.e., Ba(Zr0.84Y0.15Cu0.01)O3−δ upon a sudden change of water-vapor pressure at a fixed oxygen partial pressure are investigated via a conductivity relaxation technique. Conductivity relaxation during the hydration/dehydration process follows typical two-fold non-monotonic behavior that can be explained by decoupled chemical diffusion of H and O. However, the temperature dependence of the measured chemical-diffusion and surface-exchange coefficients is significantly different depending on the direction of the temperature change. In this study, we attempt to identify the origin of these unusual behaviors during the conductivity relaxation experiment via thorough microstructural and compositional analyses on sample surface.