I have familiarity with only one chapel in regards to a Saturday evening Mass. The priest would leave his priory Saturday morning and arrive in the late afternoon on Saturday. He offered the Saturday Mass that evening for those faithful who wished to attend that weekday Mass (attendance on First Saturdays was greater than on other Saturdays). He stayed overnight and then offered Mass on Sunday. He left to return to his priory late in afternoon on Sunday.
I am curious as to why one would think this is a sensitive issue and need to be asked anonymously. I would think this would be a question that one might easily pick up a phone a call the chapel and ask if this Saturday evening Mass was the Saturday Mass or a "Sunday Anticipation Mass". It is possible, of course, that whoever answers the phone may not even know what a "Sunday Anticipation Mass" is.