Are you saying that the Vigil of Christmas that happens on the morning of Christmas Eve, in violet vestments, is already the Mass of Christmas?

I'm clearly saying the opposite, that the "Vigil" Mass of the day before Christmas is not Christmas Mass.
You are very confused. Mass on the day before Christmas isn't actually the Vigil in the same sense as the Easter Vigil, but was merely the Mass for the day before Christmas. One of the few other "Vigils" that was retained through pre-1955 to compare it to is that of Pentecost. Rest of them slowly fell into disuse and were no longer true Vigils.
For the last time, the Vigils themselves were NOT the actual Masses of the feast, but, as the name implies, a set of services, consisting of sung Psalms, readings, etc. that went through the night in anticipation of and leading up to the actual Mass of the Feast itself. That's what the term "vigil" actually means in Latin, a night-watch. So they stayed up all night in anticipation of the Feast itself. If today there's a "Mass" on the "Vigil" of Christmas (where the term had just loosely been transferred to mean "the Day Before"), that's just because the Vigil itself felt into disuse and was no longer celebrated as a true Vigil.