The Vatican website does not state that it's other humans doing the punishing. It infers that it's God's punishment for sins and even states that in Purgatory (where man goes to be purified according to Catholic beliefs due to these sins even though the man is saved he still must go through this purification) that man must atone for these temporal sins. "those who are expiating their sins in purgatory "
Expiating means atone.
None of that points to Jesus but keeps going back to man doing something instead of relying on the Savior. There is the statement that men are forgiven yet then goes on to say that they really aren't and still need to DO something until they get to be with God. The Gospel states that we are clothed in Christ's righteousness. We are washed clean in our baptisms and this is connected to the cross where Jesus was our propitiation for sins. For all sins. Even those temporal ones. He atoned for us. We believe in this by grace through faith and get to be with God when we die.
The reader infers the writer may imply Catholic teaching is quite explicit that the temporal punishments due for sins are temporal not eternal and often earthly not purgatorial though some are purgatorial. They appear to be self-imposed or imposed by other human beings and have to do with restoring relationships within the body of Christ.
My dictionary define expiation as
the act of making amends or reparation for guilt or wrongdoing; atonement.
Your posts suggests that expiation means atone - presumably in a theological sense since you say that "none of that points to Jesus" - but it doesn't mean that precisely does it? Expiation for a crime is accepting the punishment due for it. A criminal expiates his/her crimes under civil law by serving time in prison and he/she expiates his/her broken relationships by restoring them with the help of those who were estranged by his/her criminal acts. None of this is difficult or mysterious or hard to understand.
Theological expiation is explained in the holy scriptures.
The Catechism of the Catholic Church - Glossary - says
433 The name of the Saviour God was invoked only once in the year by the high priest in atonement for the sins of Israel, after he had sprinkled the mercy seat in the Holy of Holies with the sacrificial blood. the mercy seat was the place of God's presence.25 When St. Paul speaks of Jesus whom "God put forward as an expiation by his blood", he means that in Christ's humanity "God was in Christ reconciling the world to himself."( ⇒ Rom 3:25; ⇒ 2 Cor 5:19.)
Jesus consummates his sacrifice on the cross
616 It is love "to the end"(⇒ Jn 13:1.) that confers on Christ's sacrifice its value as redemption and reparation, as atonement and satisfaction. He knew and loved us all when he offered his life.(Cf. ⇒ Gal 2:20; ⇒ Eph 5:2, ⇒ 25.) Now "the love of Christ controls us, because we are convinced that one has died for all; therefore all have died."(⇒ 2 Cor 5:14.) No man, not even the holiest, was ever able to take on himself the sins of all men and offer himself as a sacrifice for all. the existence in Christ of the divine person of the Son, who at once surpasses and embraces all human persons, and constitutes himself as the Head of all mankind, makes possible his redemptive sacrifice for all.
1475 In the communion of saints, "a perennial link of charity exists between the faithful who have already reached their heavenly home, those who are expiating their sins in purgatory and those who are still pilgrims on earth. between them there is, too, an abundant exchange of all good things." In this wonderful exchange, the holiness of one profits others, well beyond the harm that the sin of one could cause others. Thus recourse to the communion of saints lets the contrite sinner be more promptly and efficaciously purified of the punishments for sin.
