This fulfills your Christmas obligation.
It’s importance to realize that since the Second Vatican Council, the Church has allowed Masses on the evening prior to a feast to be celebrated according to the upcoming feast.
This is a restoration of the ancient belief of days beginning at sundown, not midnight.
The tradition of Midnight Mass on Christmas is venerable, but since the introduction of the possibility of Mass at a more reasonable hour, the practice of Midnight Mass has fallen into disuse in some places, in favor a a Vigil Mass.
The Local Ordinary has the right to decide the earliest possible time for a Mass to count as a vigil. In most dioceses, any Mass celebrated after 4:00 p.m. on the day leading up to a solemnity is considered a vigil, although this is not always true.
An example of an exception to the rule is today, actually. Yesterday was the Second Sunday of Advent, and today is the Feast of the Immaculate Conception. Even if a Mass was celebrated in the evening on Sunday, it would be considered the Mass for the Second Sunday of Advent, since the solemnity of a Sunday Mass supersedes that of the Mass of the Immaculate Conception in the Ordinary Form of the Roman Rite.