Actually, cycling can affect pH.
The bacteria use carbonate for their bodies, so they reduce the carbonate hardness (Kh) of the tank as they colonize.
One of the cycles in tanks, especially overstocked tanks, that limits total population IS carbonate. If the bio-load of the tank is too high there won't be enough time for the existing bacteria to decay back to water solution carbonate when they die.
Carbonate in the tank drives the pH higher. Softened water, RO and Distilled water have low pH so for replacing evaporation you can use distilled/RO and softened.
Generally I soften my water change water then build its Kh back up using Neutral Regulator (correct pH 7.0). This product contains minerals that will try to ballast the tank around 7.0 pH but may not get there completely.
If you regularly have to reduce pH because it goes way too high you can try Discus Buffer and follow the instructions on the label.
In my circumstance I ended up having to use ion resin bags to get metals out of the water because my tap water was reaching 9.0.