The meters should be fairly accurate. It could be that the P5 has a hard time regulating to that specific voltage while handling all the other aspects. If setting the unit to 121 gets you closer to 120 that’s what I would do personally.

120V rms (root mean square) doesn’t rms value depend on a sin wave. If you’re not outputting a sin wave then maybe the value is miss read rms = 0.707 of peak for a sin wave iirc

RMS does not depend on a sine wave. The RMS of any wave form can be calculated/measured.

Edit: It just occurred to me you may be referring to meters.

An analog meter calibrated for sine-wave voltage or current will not indicate true RMS when reading a non-sinusoidal wave. This is because any wave shape other than a pure sine wave has a different ratio of RMS and average values. (For a sine wave, the value is 1.1107 which is 0.707/0.636. The RMS of a sine wave is 0.707 of peak value. Its average is 0.636 of peak.)

More sophisticated digital meters can calculate and display a true RMS value, regardless of the waveform.