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Yes, Trent does explain it.

That faith is not natural, and it is not "outside the sacrament."

Trent doesn't say it's supernatural, nor that it's natural.

Trent does, as Pax states, list these as DISPOSITIONS for justification, and justification itself follows, the instrumental cause of which is the Sacrament of Baptism.

Really what's at issue is whether the Sacrament of Baptism can act as instrumental cause via the votum alone.

Trent also lists the intention to receive the Sacrament as one of these dispositions, after which "justification itself follows".

It's key that the Sacrament remains the instrumental cause even in a putative BoD.  Otherwise, you have a Pelagian system where people can will themselves into a state of justification.  Of course, when you get into all these "implicit" BoDs, including "implicit faith", the more distant the Sacrament gets from the process, the less credible it is that there's any justification being effected ex opere operato by the Sacrament itself.

Disposed = prepared for.  They have not yet been justified.

Here is Trent immediately after the section where preparation is described:

This disposition, or preparation, is followed by Justification itself, which is not remission of sins merely, but also the sanctification and renewal of the inward man, through the voluntary reception of the grace, and of the gifts, whereby man of unjust becomes just, and of an enemy a friend, that so he may be an heir according to hope of life everlasting.
Of this Justification the causes are these: the final cause indeed is the glory of God and of Jesus Christ, and life everlasting; while the efficient cause is a merciful God who washes and sanctifies gratuitously, signing, and anointing with the holy Spirit of promise, who is the pledge of our inheritance; but the meritorious cause is His most beloved only-begotten, our Lord Jesus Christ, who, when we were enemies, for the exceeding charity wherewith he loved us, merited Justification for us by His most holy Passion on the wood of the cross, and made satisfaction for us unto God the Father; the instrumental cause is the sacrament of baptism, which is the sacrament of faith, without which (faith) no man was ever justified; lastly, the alone formal cause is the justice of God, not that whereby He Himself is just, but that whereby He maketh us just, that, to wit, with which we being endowed by Him, are renewed in the spirit of our mind, and we are not only reputed, but are truly called, and are, just, receiving justice within us, each one according to his own measure, which the Holy Ghost distributes to every one as He wills, and according to each one's proper disposition and co-operation.
For, although no one can be just, but he to whom the merits of the Passion of our Lord Jesus Christ are communicated, yet is this done in the said justification of the impious, when by the merit of that same most holy Passion, the charity of God is poured forth, by the Holy Spirit, in the hearts of those that are justified, and is inherent therein: whence, man, through Jesus Christ, in whom he is ingrafted, receives, in the said justification, together with the remission of sins, all these (gifts) infused at once, faith, hope, and charity. For faith, unless hope and charity be added thereto, neither unites man perfectly with Christ, nor makes him a living member of His body. For which reason it is most truly said, that Faith without works is dead and profitless; and, In Christ Jesus neither circuмcision, availeth anything, nor uncircuмcision, but faith which worketh by charity. This faith, Catechumen's beg of the Church-agreeably to a tradition of the apostles-previously to the sacrament of Baptism; when they beg for the faith which bestows life everlasting, which, without hope and charity, faith cannot bestow: whence also do they immediately hear that word of Christ; If thou wilt enter into life, keep the commandments. Wherefore, when receiving true and Christian justice, they are bidden, immediately on being born again, to preserve it pure and spotless, as the first robe given them through Jesus Christ in lieu of that which Adam, by his disobedience, lost for himself and for us, that so they may bear it before the judgment-seat of our Lord Jesus Christ, and may have life everlasting.

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Note the council does not say that justification *may* follow preparation, it says that it *does* follow the preparation just described.
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Note also the very dense, verbose explanation-- if the truth is simply that a catechumen cannot have faith or justification before baptism, the council does everything to avoid saying just that. The Council could simply have just said what you are saying; instead, it gives a metaphysical treatment of the causes of justification, and identifies baptism as the instrumental cause, distinguishing it from the efficient and meritorious cause (both of which types of causes are metaphysically necessary, whereas an instrumental cause is *not* metaphysically necessary-- see S. Thomas). If you do not understand the significance of this distinction the council makes, I entreat you to ponder and reflect on it.
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Note everywhere you would expect the council to just slam it's fist down and identify (as those who deny the possibility of BoD identify) the metaphysically necessary administration of sacramental baptism as the only route of justification, it does something else. It hearkens the metaphysical necessity of the passion, and of the communication of the passion's merits to the Christian/catechumen. Why do you think this is, if the Council intended to deny the possibility of Baptism of Desire?
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As far as the catechumen requesting faith, this is done in the maintenance of Apostolic Tradition. It is not done out of the assumption that catechumens cannot have supernatural faith. The Council says they can. 

Note also the very dense, verbose explanation-- if the truth is simply that a catechumen cannot have faith or justification before baptism, the council does everything to avoid saying just that. The Council could simply have just said what you are saying; instead, it gives a metaphysical treatment of the causes of justification, and identifies baptism as the instrumental cause, distinguishing it from the efficient and meritorious cause (both of which types of causes are metaphysically necessary, whereas an instrumental cause is *not* metaphysically necessary-- see S. Thomas). If you do not understand the significance of this distinction the council makes, I entreat you to ponder and reflect on it.

This "verbose" explanation is there precisely to hit all the points related to rejecting the various Protestant errors (and also their distortions of Catholic teaching).

You can stop with the mansplaining here ... "If you do not understand the significance of this distinction the council makes, I entreat ..."

I entreat you to get off your high horse pretending that you alone truly understand the Council.