And, tetrachromats are the daughter of a man who is an anomalous trichromats and a woman with normal vision. One of the man's cone types has a mutation that makes it a little off.
In a normal woman, she'll have two x chromosomes, each having functionally identical coding for red, green and blue cones. She doesn't need both, so one of the x chromosomes will be switched off.
In a tetrachromat, she'll have two x chromosomes, but only two of the three types of cones are functionally identical, and the third color of cone is functionally different.
So, she might have R0, G0, B0 on one and R0, G1, B0 on the other.
When the x chromosomes are switched off, it's not always the same one. Sometimes it's the one from mom, sometimes the one from dad. So, her eyes will have R0, G0, G1 and B0.
This is what gives her superior color vision.
It also gives her a higher probability of having colorblind male children.