1. That the primary objects of faith be explicitly identified by the intellect, and firmly and unhesitatingly adhered to,
2. That the secondary objects of faith be assented to at least implicitly, by the will purposing to believe whatever authority reveals.
Those secondary objects can be believed implicitly, but the key in your quote is what i have bolded; they do so because they have what's called the formal motive of faith, the authority of God revealing.
My contention is that while this can suffice for Catholics (who do not know one or another article of Faith), the Protestant formal motive of faith is inherently defective and does not suffice for supernatural faith ... as per what you cited later from St. Thomas.
St. Thomas says elsewhere that the true rule of Faith is the authority of the Church, for a book, any Book, even Holy Writ, is incapable of resolving disputes. The Angelic Doctor points out that Scripture already shows (Mat 18:15-18) that all Christians must subject themselves to the judgment of a visible Church, a Church built on St. Peter.
This is why the formal motive of faith is inherently defective for Protestants. In order for us to know a supernatural truth with the certainty of faith, our formal motive must have the certainty of faith, and just because a Protestant says he believes some truth based on the authority of God in the Scripture, for instance, that is still a fallible rule which ultimately reduces to private judgment and therefore lacks the certitude of faith. If the formal motive does not have the certitude of faith, the object of that faith (i.e. the supernatural truths) are not themselves believed with supernatural faith, but based on human knowledge and human certitude.
Let's take a Catholic who rejects a dogma of the Church, just one. Let's say he does it with complete sincere conviction, honestly believing that the Protestants were right about one thing or another and the Church got it wrong. That person loses the supernatural virtue of faith. He believes in EVERY OTHER dogma except for the one he denied, but he loses faith because he no longer believes them with a supernatural formal motive of faith, the infallible authority of the Church. Protestants, however, believe maybe 50% of what Catholics do (just to throw a number out there), but they can have a supernatural motive of faith whereas this aforementioned individual cannot? There's no difference. Protestants similarly lack the supernatural formal motive of faith.
Formal / material heresy is a related subject that I'll come back to later (as per the St. Augustine quote).