Perhaps I can help your puzzlement (I will try anyway).I'm a bit puzzled by this. Here are my quotations from Aquinas:
'It is wicked and cruel to hand an innocent man over to suffering and death against his will. Nor did God the father so treat Christ in whom he inspired the will to suffer for us. God's severity is thus manifested; he was unwilling to remit sin without punishment, as the Apostle intimates when he says, 'He did not spare his own Son.' But it also illustrates God's goodness, for as man was unable to make sufficient satisfaction through any punishment he might himself suffer, God gave him one who would satisfy for him. Paul stresses this, saying, 'He has delivered him for us all,' and 'God has established him [Christ] as a propitiation by his blood through faith.'
[Quest. 47, art 3. Italics and square brackets in the original, underlining mine]
And
'By sin man contracts a twofold obligation. First, he is bound in slavery to sin inasmuch as 'everyone who sins is a slave of sin, and by whatever a man is overcome, of this also he is the slave. Because then, the devil had overcome man by inducing him to sin, man was delivered into the bondage of the devil. Secondly, by sin man was held to the debt of punishment according to divine justice......
As therefore Christ's passion provided adequate, and more than adequate satisfaction for man's sin and debt, his passion was as it were the price of punishment by which we are freed from both obligations. satisfaction offered for oneself or for another resembles the price whereby one ransoms himself from sin and from punishment.....Now Christ offered satisfaction.....by giving the greatest of all things, namely himself, for us. For that reason, the passion of Christ is said to be our ransom.'
[Quest. 48, art 4. Italics in the original, underlining mine]
Moreover, right at the end of Question 47, Aquinas writes: Reply to Objection 3: Christ, indeed willed His Passion just as the Father willed it; yet He did not will the unjust action of the Jews. Consequently Christ's slayers are not excused of their injustice. Nevertheless, whoever slays a man not only does a wrong to the one slain, but likewise to God and to the State; just as he who kills himself, as the Philosopher says (Ethic. v). Hence it was that David condemned to death the man who "did not fear to lay hands upon the Lord's anointed," even though he (Saul) had requested it, as related 2 Kings 1:5-14.
Here Aquinas is saying that although God the Father willed the passion of Christ, that did not excuse those who killed Him. In this Aquinas is in line with Acts 4:26-28. But in the extracts above it is clear that he believes that God 'was unwilling to remit sin without punishment' and that Christ took that punishment upon Himself.
Aquinas was clear (without a doubt clear based on the pains that he took to explain his "satisfactory punishment") that he considered the idea one could be punished (simple punishment) for the sins of another to be unjust.
So you are correct that Aquinas believed punishment necessary. But you are wrong that this is the same thing those who hold the Theory of Penal Substitution consider when they use the word.
I won't look it up now (it's on my computer) but if you cannot find where Aquinas discusses "simple punishment" vs. "satisfactory punishment" let me know and I can help. That said, I'm sure you are capable.
Perhaps the best example would be the RCC idea of penance. It is the same (I can't be punished for my father's sins but I can take upon myself a type of punishment in a satisfactory way for his benefit). When it comes to Aquinas simply think "divine penance".