Suppose there was an alternate-reality where humans evolved to see only UV light and were immune to significant amounts of UV radiation. These humans look just like us and consider it a copy of this world.
How might this world look different than ours in terms of technology such as computer displays and other items that might be different if we saw in this wavelength?
I think only a few things would change in terms of technology.
One think you don't state is which frequency, or frequencies, of UV light they see. If it's a single frequency, then no colour TV; if it's still three different frequencies, just in the UV band, then you'd probably still have colour screens.
Light bulbs would be significantly different. Old, incandescent, bulbs emit light because they're hot, and the colour depends on the temperature — "red hot" is not as hot as "white hot" (where the peak is green, but the difference between red green and blue is too small for you to notice). If we saw UV instead of the 390-700 nm we really see, incandescent bulbs would need to be much hotter to have the same apparent brightness, but they can't be made much hotter than they already are before they melt.
Therefore, instead of incandescent bulbs, you would have fluorescent bulbs. Fluorescent lights work differently, emitting UV light to start with and then converting that (by fluorescence) into visible light. Your alternate-reality humans probably wouldn't need to convert it, depending on the frequencies they can see and how broad the UV spectrum is (for all I know they may be monochromatic UV light sources, which would make them look as weird to your people as pure green LEDs look to us).
Outside of the technological limits, the world would be hazy. UV light is absorbed more strongly by the atmosphere than visible light, creating a blueish haze that photographers try to avoid by putting UV filters over their lenses. The effect gets worse as you go deeper into UV. At the extreme, you wouldn't be able to see anything because it would be like being inside the thickest, darkest, cloud you can imagine.
The only significant difference is that the UV-humans would use a different formula for making glass. They'd used fused quartz glass, instead of soda lime glass.
Ultraviolet (Wikipedia)
Florecent lights would not need a florecent coating as they would see the mercury vapor emissions directly. So it would not be called florecent lights.
The uv band is much wider than visible light. VL is about 1 "octave" from 400 to 800nm. UV is from 10 to 400 nm, or about 5.3 octaves.
If these creatures had evolved to see in UV light, they may need a greater range of colour detecting rods in their eyes. Their colour vision would be very different, and they may see in more dimensions of colour than we do.
Next, the atmosphere is not that transparent to UV light, especially at shorter wavelengths. This means that the atmosphere would have a very distinct colour. At a distance only those things that emitted light at the longest UV wavelengths could be seen. They may describe these as "red" but of course their experience of colour is utterly alien to us. In fact there is not much short wavelength UV light around, To them, everything would be a dim hazy red colored murk.
There are good evolutionary reasons why we see in the visible spectrum.
