With the increasing demand for artificially intelligent hardware systems for brain-inspired in-memory and neuromorphic computing, understanding the underlying mechanisms in the resistive switching of memristor devices is of paramount importance. Here, we demonstrate a two-step resistive switching set process involving a complex interplay among mobile halide ions/vacancies (I-/VI+) and silver ions (Ag+) in perovskite-based memristors with thin undoped buffer layers. The resistive switching involves an initial gradual increase in current associated with a drift-related halide migration within the perovskite bulk layer followed by an abrupt resistive switching associated with diffusion of mobile Ag+ conductive filamentary formation. Furthermore, we develop a dynamical model that explains the characteristic I-V curve that helps to untangle and quantify the switching regimes consistent with the experimental memristive response. This further insight into the two-step set process provides another degree of freedom in device design for versatile applications with varying levels of complexity.