Let me explain: our eyes perceive RGB, but we don't in consciousness -- the RGB is mapped somewhere, long before consciousness, further in the brain to more of a perceptual RYGB -- a two-dimensional space of warm/cold (RY/GB) against "lighter/darker" for lack of a better term (YG/RB). See [1] for more info. Psychologically yellow functions as a primary color even though we don't have a rod for it. (In reality it's much more complicated than this, since we perceive saturation, brightness, etc. but this is a valid simplification for current purposes.)
So it's entirely possible that tetrachromats map their four rods to the same RYGB box the rest of us perceive as qualia, only with a different mapping. Then, they can still distinguish between colors everyone else sees as the same (because different spectra), but they'll still perceive them as the same color qualia the rest of us perceive -- colors in the world will just be mapped slightly differently. The closest (but imperfect) analogy I can think of is wearing polarized glasses -- same color gamut, but certain things "compare" differently now.
Or, does tetrachromacy somehow also change the perceived-qualia RYGB model itself? So there's, say, a 3rd axis beyond warm/cold and "lighter/darker"? Or the span of the two axes somehow becomes wider to accomodate more information? Or something else?
Hope this is clear. Perhaps it could be tested psychologically, though -- simply by asking participants to describe the colors they see qualitatively, to see if the words they use in color comparisons (e.g. warmer/colder) are the same as those used by the rest of us... or if there's any new "feeling" component involved.
[1] https://en.wikipedia.org/wiki/Opponent_process - "...the cells were widely called opponent colour cells, Red-Green and Yellow-Blue. Over the next three decades, spectrally opposed cells continued to be reported in primate retina and LGN."