First, they are optional.
There is no requirement to have a Vigil Mass, and no requirement to use the text if the Mass is "the evening before." The one exception, of course, being the Easter Vigil which is required.
A priest could use the Mass for the day itself, even though a Vigil Mass is available.
Note: I don't recommend or advocate it, I'm simply saying that it would not be illicit to do it.
The original purpose of a Vigil Mass was that it was a Mass in the night before a feast. "Vigil" means to stay awake. They weren't merely evening Masses but Masses during the true nighttime.
Unfortunately, over the centuries, vigil Masses kept getting earlier and earlier. By the time of Vatican II some were actually celebrated in the morning of the day before the feast. The Council called for a reform of liturgical times to better match the actual time of day of the celebration. At present, the Roman Missal says that they are celebrated "in the evening" the day before the feast. There is a rubric accompanying the vigil Mass texts in the Roman Missal (that's the source you're looking for) that explain this. I don't think it's meant to exclude nighttime, but I do think it's meant to exclude morning or afternoon.
Here's the exact text of the rubric in the current Roman Missal for the Vigil Mass of Epiphany
This Mass is used on the evening of the day before the Solemnity, either before or after First Vespers (Evening Prayer I) of the Epiphany
The Saturday evening Mass is not the "anticipated Sunday Mass" it is the festive Mass of Sunday. The Church makes no distinction between the Sunday Mass celebrated on Sunday morning and the Sunday Mass celebrated on Saturday evening--both are equal and identical in every respect. The notion of an "anticipated Mass" is a holdover from the 1917 Code of Canon Law which was completely changed by the 1983 Code. Unfortunately, we sometimes hear the old terminology, and more importantly, the old ideas used, even though they no longer express the Church's position.