Physical mechanisms underlying the multilevel resistive tuning over seven orders of magnitude in structures based on TiO2/Al2O3 bilayers, sandwiched between platinum electrodes, are responsible for the nonlinear dependence of the conductivity of intermediate resistance states on the writing voltage. To improve the linearity of the electric-field resistance tuning, we apply a contact engineering approach. For this purpose, platinum top electrodes were replaced with aluminum and copper ones to induce the oxygen-related electrochemical reactions at the interface with the Al2O3 switching layer of the structures. Based on experimental results, it was found that electrode material substitution provokes modification of the physical mechanism behind the resistive switching in TiO2/Al2O3 bilayers. In the case of aluminum electrodes, a memory window has been narrowed down to three orders of magnitude, while the linearity of resistance tuning was improved. For copper electrodes, a combination of effects related to metal ion diffusion with oxygen vacancies driven resistive switching was responsible for a rapid relaxation of intermediate resistance states in TiO2/Al2O3 bilayers.