The diocesan marriage tribunal simply looks at the circumstances, notes that according to the code of canon law no marriage ever took place due to a lack of jurisdiction, and rubber stamps it.
They're wrong though. Even if the priest didn't have jurisdiction that doesn't mean you just divorce the couple and pretend the whole thing doesn't happen. In normal times, such marriages would be convalidated by proper authorities. There is the small matter of THE NATURAL LAW by which marriage is between 1 man and 1 woman, for life, for the begetting and raising of children, etc.
See? Here, the Novus priests, too, are thinking "divorce" while they claim to be talking about annulments and Catholic marriage validity. It's all a sham. As I said above, the couple thinks of and treats "annulments" like divorce. They take all the cultural structures, terms, etc. around the institution of divorce and put a Catholic costume on it, called "annulment". Novus priests and marriage tribunal canon lawyers do the same thing. They know this couple "wants to move on" -- in modern world terms, they "want a divorce" so they're thinking in those terms. They're thinking with a non-Catholic mindset.
When Catholic missionaries converted a village of pagans, they didn't say, "Ok, everyone, you're now single! Pick whatever partner you want for your new Catholic marriage, which is for life this time so pick wisely!"
Rather, they convalidated the NATURAL LAW marriages which had already taken place. There are still emotional, psychological, and familial bonds which are very real. God designed the sexual union so that various bonds would form between the man and the woman. Also, there is the whole dimension of children, who are usually quite attached to their parents and vice-versa.
The nature of the sacrament of matrimony is that the man and the woman confer the sacrament upon each other. The priest is only a witness for the Church. Some small technicality like a lack of jurisdiction wouldn't change all the monumental family and relationship-building that already took place.