Using non-brand oil for cleaning brake pistons
Probably yes.
I am expecting them to have very different viscosity and boiling point, so I would rather not.

The idea is to have an homogeneous oil if some droplets are left over after the cleaning process (same oil in same oil).
However, it should be no problem if you use a different mineral oil. At worst, the different oil will hamper your braking effectiveness, at which point you will need to flush out all the oil from the brake circuit.