The dynamics of the H2O2–Na2S2O3–H2SO4–CuSO4 homogeneous pH oscillator was studied in the flow reactor potentiometrically using different sensors: platinum electrode, Cu(II) ion‐selective electrode (Cu‐ISE), and pH‐electrode. It was found that for the flow rates close to two bifurcation values, between which the oscillations exist, there is a detectable phase shift between the response of the Cu‐ISE and other electrodes, while it practically vanishes for the intermediate flow rates. To explain both the oscillations of the Cu‐ISE potential and the relevant phase shift, the system's dynamics was studied both experimentally and numerically. The literature kinetic mechanism of the pH oscillator was extended for the dynamics of the copper(II) and copper(I) species in the form of thiosulfate complexes, and kinetic parameters of the redox equilibria, ensuring the oscillations, were estimated. It was found that the phase shift at the relatively low flow rates occurs due to limited efficiency of the supply of CuSO4 catalyst, as the species of lowest concentration, to the reactor, and therefore it can be minimized either by increasing the flow rate of all reactants or, alternatively, by enhancing the model concentration of CuSO4 in the feeding stream, for its fixed flow rate. This work is one more proof that it is useful to monitor the dynamics of the homogeneous oscillatory systems with more than one electrode, if the experimental potential–time courses are to be explained in terms of an appropriate kinetic mechanism.