That is, in fact, a good point, in that the few women with this ability (it's x-linked, you have to have two 'x's to have it, and even having both kinds of gene isn't enough) were discounted for years by (mostly male) doctors.
This was something new to me, so I had to go do a little bit of reading. Humans normally have three distinct photopsin proteins in the cones, for sensing color:
The long-wavelength (red) photopsin is coded by a gene (OPN1LW) located on chromosome X.
The middle-wavelength (green) photopsin is coded by a gene (OPN1MW) also located on chromosome X.
The short-wavelength (blue) photopsin is coded by a gene (OPN1SW) located on chromosome #7.
Males and females alike have two copies of chromosome #7. Females have two copies of chromosome X, however normally one of the two copies is inactivated early during embryological development. Males have just one copy of the X.
To first explain why males are more likely to be color blind vs. females, the reason is that with females there is high likelihood that at least one of the two copies of the X chromosome will have the non-recessive version of the gene (whichever of the two genes it is for which a recessive version is common). This is entirely the same as with the explanation of why hemophilia is less common in females than in males. Owing to X-inactivation (by virtue of which females and males produce similar amounts of proteins encoded on the X chromosome), each cone cell will have one active copy of the X chromosome. The other copy is present in the nucleus of the cell, but has been inactivated. Notwithstanding that X-inactivation occurs early in embryological development, the choice of which copy is inactivated is sufficiently random such that in each eye (of a given female) the copy that is active in some cells is the copy that is inactive in other cells. Thus, both copies of the X chromosome are active in each eye, notwithstanding the X-inactivation. (In other words, it isn't common, apparently, to find females where one of the two eyes is color-blind and the other isn't. I need to say, though, that I haven't looked into this question nearly to the extent that I should have before writing this.)
With respect to the understanding of the tetrachromatic effect encountered in a small percentage of females, I have just run into two conflicting explanations, that differ with respect to whether this phenomenon is related to the long-wavelength photopsin or the medium-wavelength photopsin. This is where it gets tricky, and interesting. All accounts agree that in a small percentage of women, OPN1MW (green) is accompanied by the similar gene OPN1MW2. Essentially, a small percentage of women have two copies of what is essentially the same gene. In some accounts the indication is that by virtue of having an extra copy of this gene (on at least one copy of the X, not necessarily both), they acquire the effect. Other accounts say that the variation in peak sensitivity for the different alleles of either of these two genes is too weak to account for the effect. Instead, the effect is due more simply to the large number of alleles of the long-wavelength gene OPN1LW (red), where the variation in peak sensitivity, for the different alleles, is much greater than it is for the two medium-wavelength genes combined.
With either of these two candidate explanations, the underlying question is why the effect is specific to women, which is to ask, how does the number of copies of the X chromosome enter in to the explanation? A female who has the duplicated gene on both copies of the X could potentially carry four distinct alleles for the gene OPN1MW. But if the variation in peak sensitivity is weak for the alleles, this wouldn't produce the effect, regardless of how these four alleles are distributed over individual cone cells. On the other hand, all females have two copies of OPN1LW, whereas males have only one. As such, the peak sensitivity for red light will be the same for all red cone cells in a given male. Whereas for females, who have two copies of this gene, the peak sensitivity for red light would be different for different red cone cells, if the two alleles they received are different with respect to the peak sensitivity.
It thus seems likely that while the explanation certainly does involve the fact that females have two copies of the X whereas males just have one, that it likely is not related to the fact that some X chromosomes carry an extra copy of the OPN1MW gene. Rather, it is more likely explained by the fact that females have two different versions of OPN1LW, vs. one version for males, and that the number of alleles of this gene is sufficiently great for there to be significant variation in the peak wavelength sensitivity, such that in some females, some of the cells that sense red are most sensitive to one specific wavelength whereas other cells that sense red are most sensitive to a different wavelength, with the difference in peak sensitivity sufficient to provide the brain with the ability to make accurate distinctions in hues of red, more accurate than is made possible by the weak sensitivity that the green cones have, to red wavelengths.