If there was a whole 24-hour period during which the sun was on the celestial equator, then 12 hours would be day and 12 night (going by the time the centre of the sun's disc rose and set).
But the sun is always moving along the ecliptic, so the day we call the equinox is just the 24hr period within which the sun crosses the equator, which is an instantaneous event.
Perhaps you would accept phrasing the sentence in question as saying the Earth-Sun axis is doing these two things?
Article starts out by specifying the time of the event
It gives the impression that, geometrically speaking, there is a day on (or near) the equinox which has equal darkness and daylight. Of course, this isn't guaranteed at all, and certainly not for every point on the earth's surface.