cishet dude brain over here but this confuses me, wouldn't this person be intersex and not a "cis" woman?

You can be inter and cis (or inter and trans, i know several inter trans women). These are just completely different phenomena.

Inter (and its opposite, endo) is a purely biological category. Cis and trans are purely psychosocial ones, as they just mean if your gender identity matches your assigned gender at birth or not. Inter people can be men, women or nonbinary. If a person gets assigned female at birth, is raised as a girl, and identifies as a woman throughout her life, she doesn't stop being cis when she learns that she had XY chromosomes or internal testes all along, because she meets all the criteria of being cis. It just means she's an inter cis woman instead of an endo cis woman.