Thank your this link. It tells us that:
"Dominican Cardinal Christoph Schönborn was one of the first to apply Aquinas’ supposed imprimatur to the document, telling reporters at a press conference to mark its publication in April that the document “is profoundly Thomistic.” The Pope has designated the Archbishop of Vienna as the definitive interpreter of the exhortation."

I am not sure why we should prefer Fr Cole's claim to Schönborn's, or vice versa. Fr Cole tells us that "In the end, following Tradition is the most authentically Thomistic position, for he firmly opposed any doctrinal position that was not faithful to divine revelation and the Church’s binding teachings." The teaching from Francis is now part of our tradition, and Schönborn is the one faithful to it. Fr Cole seems rather to side wih those who claim it is not, so it appears this principle depends on prior position. If you believe papal teaching is part of our tradition, you side with Francis; if not, you side against.