Do you have evidence of that?
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Baptism always comes first, as it is the gateway to all other sacraments; the baptismal character imprints the character of Christ the Eternal priest, which alone allows and entitles one to participate in the Church's sacramental life.  Moreover, the Church passes judgment on the penitent in confession, but she has no jurisdiction over the unbaptized, so...
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Just what an acquaintance told me.  He entered the NO church a few years ago.  According to him, they started having classes around September, and then in March, a few weeks before Easter, the NO priest who was teaching the class had each person in the class make their first Confession.  Following this, at the Easter Vigil, they were each baptized, confirmed (by the NO priest), and received Communion.

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Well if he really wasn't baptized then that was a gross abuse.  If he was a Protestant whose baptism was certainly valid, though, it would have been quite different.  If he was an unbaptized or doubtfully baptized convert, though, the confession-before-baptism unfortunately meant nothing.

Well, the only scenario in which I could see this even possibly making sense is if there's DOUBT about the validity of his Baptism.  In that case, in the event that it actually WAS valid, the conditional Baptism would be of no avail toward the remission of sins, and Confession would have been required.  Except that I've never heard of a conditional Confession.  Nor should a Confession be heard until someone has entered the Church.  So the proper order would be conditional Baptism, Confession that included all sins even before Baptism, Confirmation, and Holy Communion.  Except in the Novus Ordo they like to be dramatic, so stopping their festivities to have someone make a Confession right after Baptism would ruin the party.

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Suppose a priest finds himself in a situation where he might grant absolution to a dying man but is unsure if he's actually alive.  Say, the man elicits a "sign" that he wishes to confess (like in a last rites scenario) but is unable to do so and as soon as the priest begins the absolution formula he is unsure if the man is still alive (maybe a piano falls on him, I don't know, it's a hypothetical to help tease out the principle).  Perhaps the priest would conditionally absolve in such a case "if you can be absolved, I absolve you, etc."  That's the only theoretical way I can imagine there being such a thing as conditional confession, and it doesn't seem like it'd apply to the OP's scenario.  The traditional practice for doubtful baptisms is conditional baptism followed by "regular" confession."

In general I don't think there's such a thing as conditional confession.  When I've confessed things which I weren't sure whether they were sinful, I've had priests ask me to confess something from my past that I was sure was sinful before they would give absolution.  This implies that absolution should only be granted, at least in ordinary circuмstances, if the priest is sure the penitent has sins to confess.  If the priest isn't sure then he either shouldn't absolve or should encourage the penitent to confess something certainly sinful, even if previously absolved.

The traditional practice for doubtful baptisms is conditional baptism followed by "regular" confession."

Ah, but would this regular confession have to cover the person's entire life or just from the time of the conditional Baptism?  If you're a probabilist, the existence of sins necessary to confess is in doubt, so therefore no strict obligation to confess them.

So do I understand correctly that if a man who was never baptised commits murder, then gets baptised, he never has to confess the murder?

That's correct, he does not need to confess that sin or any sin committed prior to being baptized in order to be forgiven of it.

Trent's Catechism teaches:

All Sins That Precede Baptism

When we first make a profession of faith and are cleansed in holy Baptism, we receive this pardon entire and unqualified; so  that no sin, original or actual, of commission or omission, remains to be expiated, no punishment to be endured. The grace of Baptism, however, does not give exemption from all the infirmities of nature. On the contrary, contending, as each of us has to contend, against the motions of concupiscence, which ever tempts us to the commission of sin, there is scarcely one to be found among us, who opposes so vigorous a resistance to its assaults, or who guards his salvation so vigilantly, as to escape all wounds.


The Council of Trent teaches:
"For, *in* those who are born again, there is nothing that God hates; because, there is no condemnation to those who are truly buried together with Christ by baptism into death; who walk not according to the flesh, but, putting off the old man, and putting on the new who is created according to God, are made innocent, immaculate, pure, harmless, and beloved of God, heirs indeed of God, but joint heirs with Christ; so that there is nothing whatever to retard their entrance into heaven."