I noticed that noise that I can hear through headphones is inaudible through a quad box.
That's another test, using head phones, that is not how your going to use the amp.
However what I'm more concerned about is that the opposite volume affects the channel that I'm plugged into.
But one volume should not affect the volume of the other channel.
Although I think that Sluckey's probably right, you have something wired wrong, I also think below is part of what your hearing and is normal.
Many amps have 'interactive' volume controls. If you plug into 1 channel and turn up the volume of the other channel it will effect the tone and/or the distortion/drive of the amp.
A Fender tweed deluxe, 5E3, is famous for this. Neil Young had a rig made with servo motors and memory settings to turn the volume controls live on stage during songs to use this. He has foot switches for the different pre programed settings he likes. He's been using this rig live for at least a few decades.
I attached a highlighted schematic of the 1 you posted showing this on your amp.
The red is the normal channel output going to the 2nd stage tubes gird input. But that pF cap/C6 across the 470K mixing R on the other has at least 3 different paths to ground depending on where that bright channels volume is set.
When the bright channels volume is off/0 then the signal that goes back through the 470pF/C6 cap goes to ground.
If you turn the bright channel volume up all the way now you will bypass C5 and go to the 22nF cap/C4 to the 100K plate R then through the B+ filter cap to ground.
This is why your having the problems plugging into the normal channel, input 2, because when you plug into the bright channel, input 1, there's no 470pF bypass cap across that channels 470K series mixing R. So it has only the 470K mixing R to bleed through and that 470K value is giving good isolation from the other channel.
The orange line shows where to break that 'bleed' path. That's what you did when you lifted 1 end of that cap.