During the modified salinity water (MSW) flooding, the injected water must first reach and interact with the residual oil attached on the pore surfaces through a thin formation water film to mobilize the oil and improve the oil recovery. This can cause a delay in the rock response to the injection of MSW, as observed in many core flooding tests. The physicochemical processes that control this response time occur at two different scales: the alteration of wettability at the film scale and the consequent mobilization of oil at the Darcy scale. We propose a new model that links the diffusion- and adsorption-controlled flow of ions in the thin film to the two-phase flow of oil and water at the Darcy scale through a wettability-modifier parameter. This parameter is defined based on the salinity change in the water film or the adsorption/desorption of ions on the water-film-covered rock and is used as an interpolating parameter for two sets of relative permeability curves for the initial state and the new state of the reservoir. We utilize the model to analyze several core flooding results to first explain the observed oil breakthrough delay and second find out how much of this delay is expected to happen in the reservoir scale. Our results suggest that sizes of residual oil droplets and the effective ionic diffusion in the thin water film, dictated by the electrostatic charge of the oil-brine and rock-brine interfaces, play significant roles in controlling the oil breakthrough time. In addition, our observations suggest that the observed delay is strongly controlled by a rather slow diffusion process in the water film, which is not scalable from the core to field scale.