You are correct and I'm quite aware of the sciecne behind quantifying color vision in humans. I'm a spectroscopist who had to write software to quantify color, amongst other things, for the business I'm in. It's easy to represent color in a variety of 2 dimensional color coordinate systems like L*a*b* (a*b* being the color portion, L* representing the lightness or darkness of a color). Imagine how much more complicated that would be for a tetrachromatic system? That would be color in 3-dimensional coordinates with a fourth dimension for lightness. Very difficult to mentally visualize. Our color wheel would essentially be a 2D surface in a 3D color space. You would have UV mixed with the other 3 primary colors. So you could have yellow, blue and red, their combinations and then all of those combinations with various amounts of UV. You could have UV+blue as a new color, as well as UV+red and UV+yellow. The vividness of an avian vision system must be incredible. The authors in the article attempted this very thing by estimating the spectral response and luminosity of a given object based on avian photoreceptor sensitivity would have in this color space and see if the birds could distinguish it from other UV-color objects. The theory matched the bird behaviour very well.
Since we lost the color receptors and then gained one back, I wonder if our brains neurologically could process a tetrachromatic color system.
Entering the twilight zone of pure speculation: humans experience color temperature as a banded gradient. It is fairly easy to demonstrate that the bands of the rainbow have no object reality, and yet we see seven or so fairly distinct bands. If color information is coded as neural firing rates, the bands could be heterodynes.
If we had more color receptors, we might experience more "primary" colors. Do you happen to know how how many rainbow colors are seen by colorblind people? I am a bit embarrassed asking this, because my son is red-green colorblind.
I think children have enough plasticity in brain function that they might be able to handle a couple extra colors. For an adult, it would be sorta like learning a new language, never fully fluent, and always with an accent...