Here is a clear explanation from St Robert Bellarmine, posted by Siscoe/Salza (of all people).
Another way to understand it is that the minister does not have to intend what the Church intends, but only what the Church does. The object of his intention is the action or ceremony performed, not the purpose of the action. Bellarmine explains:“The Council of Trent does not mention the purpose of the sacrament or say that the minister ought to intend to do what the Church intends but what the Church does. Moreover, what the Church does refers to the action, not the purpose. There is required the intention with regard to the action, not in so far as it is a natural action, but in so far as it is a sacred action or ceremony, which Christ instituted or Christians practice. If one intends to perform the ceremony which the Church performs, that is enough.” (Bellarmine, de Sacramentis in genere chapter 27.) link
He continues:
"There is no need to intend to do what the Roman Church does; but what the true Church does, whichever it is, or what Christ instituted, or what Christians do: for they amount to the same. You ask: What if someone intends to do what some particular or false church does, which he thinks the true one, like that of Geneva, and intends not to do what the Roman church does? I answer: even that is sufficient. For the one who intends to do what the church of Geneva does, intends to do what the universal church does. For he intends to do what such a church does, because he thinks it to be a member of the true universal church: although he is wrong in his discernment of the true church. For the mistake of the minister does not take away the efficacy of the sacrament: only a defectus intentionis does that." (Bellarmine, de Sacramentis in genere chapter 27 paragraph 8, translated by Fr. Hunwicke).
The simplest way to understand it, is that the general intention “to baptize” (whatever that means), or “say Mass” (whatever that means), or to “ordain a priest” (whatever that means), is sufficient to produce the sacramental effect – even if the one administering the sacrament publicly denies the effect that the sacrament is intended to produce (e.g., washing away Original Sin, changing bread and wine into the Body and Blood of Christ, etc.)..
What will render a sacrament invalid is the positive intention not to do what the Church does. This was addressed by the Holy Office under Pope Alexander VIII, which condemned the following proposition:
“A Baptism is valid when conferred by a minister who observes every external rite and form of baptizing, but within in his heart, resolves to himself: not to intend what the Church does.” - CONDEMNED, (Pope Alexander VIII, Decree of the Holy Office, December 7, 1690, Errors of the Jansenists, Denz., 1318).
If the minister seriously intends to perform the religious ceremony, or the ceremonial action, and does not positively withhold the intention to do what the Church does, the validity of the sacrament will not be in doubt due to a defect of intention.---
Conclusion - The Catharinus view is obviously wrong as they denied the necessity of ANY intention by the minister. Pope Alexander's condemnation is obviously correct but the error condemned is more specific than the general error of the Catharinus. Once I read the catharinus view, I understood better the truth being protected and the error.
In my opinion, the condemnation as it is written needs more context to understand the purpose/truths. Which context I did not have earlier in this thread. For that, I apologize.