This is why we can see as many colours as we do: each type of cone has a different peak frequency that activates it most, but still responds to an entire range. These ranges overlap. So a colour often stimulates two or three types, and it's the relative amount of stimulation determines the colour we see. So if a light stimulates the "red" cones a lot more than the other two types, it looks red. If the "red" cones are stimulated a little more than the others, the light looks yellow. Etc. It's the comparison that matters.
So, the reason purple and blue look different is because purple causes the blue cones to be stimulated a lot more than the other two types of cones, and with blue the difference is less. In both cases the blue cone is stimulated most, but with purple the difference is greater.
There are special cells in the retina that sort out all this information and transmit the message to the brain. If you're curious about reading more about this you can google "opponent process theory".
The question you asked - whether the tetrachromacy test would work on an RGB computer monitor - was debated in the comments section of the webpages I linked to. It seems to me it could. If the concentration of red, green and blue pixels was different, the relative amounts of stimulation of each type of cone would be different. And two slightly different types of "red" cones would allow more distinctions to be seen.