Using electrolysis of water as a proton generator
In a chemical sense, "anode" of an electrolytic cell is the most powerful oxidizing reagent known, so much so that it oxidize F(-) to elemental fluorine. Don't forget that the electron balance in an electrolytic cell is always maintained so the gram-equivalents of x reduced at the cathode must equal gram equivalents of y oxidized at the anode. As a result, half cell reactions cannot occur alone. So something is being oxidized at the anode, this is your nickel electrode. Platinum is the best one but it is too expensive. Graphite electrode might be an economical substitute. Secondly, you have to add an electrolyte to the anode chamber as well because tap water resistance is pretty high. You can add a non-corrosive electrolyte such as sodium sulfate. With these changes, hopefully you will see the desired trend.