12 psi is the cold start pressure. As water heats it expands and presses against the precharged bladder. At full temp of 180 degrees the system will normally be in the low 20's in pressure.
A bigger tank may drop the upper end 2 PSI at most, but not needed.
All is good with your system. Don't touch a thing.
If the pressure didn't increase when heated, you would experience flashing and pump cavitation that you don't want.