We recently replaced the "ARMOUR" letters to be a consistent shade of white. The customer says it looks fine to the naked eye, but on camera the ARM and OUR sections are two different temperatures. I believe those sections are powered by two different transformsrs. These letters were all made from the same box of glass. Is this transformer related? If so, why does it only appear on camera and not in person?

If the shutter speed of the camera is close to the power frequency being applied to the tube (or an even multiple) then it becomes possible to capture it during a point where the ac waveform is rising or falling and potentially be able to effectively "stop" the visual effect. This is why you can sometimes get part of a sign to appear on and part off in a single photo even though visually it all appears to be illuminated. Add to this that the cameras have a wider dynamic range than what you can see with the naked eye and you can easily create a situation where things will appear different. (You could, for example, be seeing a situation where the phosphor is emitting on the down cycle while the other is closer to the peak of the waveform.) At least that's a good guess without knowing any really specific information on the types/number of transformers and how the load was divided up.  To mitigate this, try using a different shutter speed and aperture combination or even a different speed of film or iso setting.