Don’t be fooled by those who tell you this. Although the word equinox may be Latin for “equal [day and] night,” the length of each is not exactly 12 hours during the autumnal equinox.
Those days are called equiluxes, and they are entire days, not specific moments, as equinoxes are. The actual date of equiluxes varies depending on where you are in the world, but they typically occur a few days after the fall and spring equinoxes.
Equinoxes and equiluxes happen days apart because of the Earth's atmosphere, which bends the sun's light so that days are still longer than nights at the equinox. It takes a few more days for day and night to even out.
On equinoxes, however, the sun does rise and set directly in the east and west.