It took a very patient EE to give me an idea about where hum comes from and how it gets eliminated. Wall warts are notorious for passing on the hum from wall current, but it can come from RF and probably other sources. Pedal board power supplies usually have some filters built in to lessen the effect of at least the wall current. That lessens but does not eliminate the noise. To complicate matters, a lot of pedals have a small amp in them. Sometimes these little amps can pretty dramatically increase the proportion of signal that comes from noise rather than your playing. That might be what is happening with the headphones. They could be amplifying some noise that your amp has filters for. That happened to me with a little pedal I built. It was originally designed to run only on battery power only. When I plugged it in to wall power, it turned out that a part of the IC amp chip that was basically unused when on DC power began amplifying the hum. My EE friend showed me how to bypass this, and the hum all but disappeared--which I now know means "became mostly inaudible, but still there."