If another being had a quadchromatic visual perception system or a true-wavelength perception system, would they perceive the same colors from our trichromatic screens?
Of course not. Tetrachromacy is real, can occur in humans, and she indeed seen differently:
In 2010, after 20 years of study of women with four types of cones (non-functional tetrachromats), neuroscientist Dr. Gabriele Jordan identified a woman (subject cDa29) who could detect a greater variety of colors than trichromats could, corresponding with a functional tetrachromat (or true tetrachromat).
(From Wikipedia)
To answer your main question:
Would aliens with different visual perception be able to read our screens?
Most probably yes. As you can notice, most of the information in our screens is coded by brightness-darkness, not actual colours. So if they can register wavelengths in our visible spectrum, they will be able to read our letters and navigate our websites.
Cells are responsive in quite wide bands, for example in birds:
If aliens are somehow similar, then no matter where exactly the peak will be, they will be able to register light or no light. Of course, the further away from our peaks, the more different would computer image look from the real world one - because computer screen only emulates the parts of the real-world look we, humans, notice, and not the full spectrum. Look for emission spectrums and absorbtion spectrums of various light sources and items to see them. Item with flat absorbtion spectrum will look gray / white to both us and them. Item that reflects similar amounts of our "peak" frequencies but different amounts where our cells are not so sensitive will look white-ish for us, but not for them. And so on.