Cyril of Jerusalem, Catechesis Lecture 4, paragraph 9 says: 

'Believe then that this Only-begotten Son of God for our sins came down from heaven upon earth, and took upon Him this human nature of like passions with us, and was begotten of the Holy Virgin and of the Holy Ghost, and was made Man, not in seeming and mere show , but in truth; nor yet by passing through the Virgin as through a channel ; but was of her made truly flesh, and truly nourished with milk, and did truly eat as we do, and truly drink as we do. For if the Incarnation was a phantom, salvation is a phantom also. The Christ was of two natures, Man in what was seen, but God in what was not seen.'

Cyril of Jerusalem, Catechesis Lecture 12, paragraph 15 says: 

'The Lord took on Him from us our likeness, that He might save man's nature: He took our likeness, that He might give greater grace to that which lacked; that sinful humanity might become partaker of God. For where sin abounded, grace did much more abound.'

Cyril of Jerusalem, Catechesis Lecture 13, paragraph 2 speaks of Jesus putting away the wrath of God which is against mankind, as defined by the death which set in from the fall. Note how Cyril explains death in 13.4-6, and explains the symmetry between the fall and Jesus' death in 13.18-21, 'that he might undo the sin', and 13.28, 'that sin might die', and 13.33, 'He preserved both the truth of His sentence [of death], and the exercise of His loving-kindness.'  Thus does Cyril exposit his opening statement in 13.1, that the cross of Christ 'loosed all who were held fast by sin.' Then, see 13.28:

“He stretched out His hands on the Cross, that He might embrace the ends of the world; for this Golgotha is the very centre of the earth. It is not my word, but it is a prophet who has said, You have wrought salvation in the midst of the earth. He stretched forth human hands, who by His spiritual hands had established the heaven; and they were fastened with nails, that His manhood, which here the sins of men, having been nailed to the tree, and having died, sin might die with it, and we might rise again in righteousness. For since by one man came death, by One Man came also life ; by One Man, the Saviour, dying of His own accord: for remember what He said, I have power to lay down My life, and I have power to take it again.”

Cyril in 13.33 also indicates that the atonement of Jesus was not the violence done on him, as in Penal Substitutionary Atonement, but his voluntarily laying down his life, as in Medical Substitution. That is because we had become enemies of God because of the corruption of sin in us, and needed to die in order to not immortalize sin within ourselves. That is the problem of human nature’s condition which Jesus resolved:

“These things the Saviour endured, and made peace through the Blood of His Cross, for things in heaven, and things in earth. Colossians 1:20 For we were enemies of God through sin, and God had appointed the sinner to die. There must needs therefore have happened one of two things; either that God, in His truth, should destroy all men, or that in His loving-kindness He should cancel the sentence. But behold the wisdom of God; He preserved both the truth of His sentence, and the exercise of His loving-kindness. Christ took our sins in His body on the tree, that we by His death might die to sin, and live unto righteousness. 1 Peter 2:24 Of no small account was He who died for us; He was not a literal sheep; He was not a mere man; He was more than an Angel; He was God made man. The transgression of sinners was not so great as the righteousness of Him who died for them; the sin which we committed was not so great as the righteousness which He wrought who laid down His life for us — who laid it down when He pleased, and took it again when He pleased. And would you know that He laid not down His life by violence, nor yielded up the ghost against His will? He cried to the Father, saying, Father, into Your hands I commend My spirit Luke 23:46; I commend it, that I may take it again. And having said these things, He gave up the ghost Matthew 27:50; but not for any long time, for He quickly rose again from the dead.”

Cyril of Jerusalem, Catechesis Lecture 18, paragraph 1 says that the motivation for Christian faithfulness is not gratitude for Jesus taking the retributive justice of God in our place, but the shared hope for the resurrection:

“The root of all good works is the hope of the Resurrection; for the expectation of the recompense nerves the soul to good works. For every labourer is ready to endure the toils, if he sees their reward in prospect; but when men weary themselves for nought, their heart soon sinks as well as their body. A soldier who expects a prize is ready for war, but no one is forward to die for a king who is indifferent about those who serve under him, and bestows no honours on their toils. In like manner every soul believing in a Resurrection is naturally careful of itself; but, disbelieving it, abandons itself to perdition. He who believes that his body shall remain to rise again, is careful of his robe, and defiles it not with fornication; but he who disbelieves the Resurrection, gives himself to fornication, and misuses his own body, as though it were not his own.”

Cyril says in 18.4 that God must reward and punish people according to their deeds, thus arguing again for resurrection. But to Cyril, God will apparently judge each person personally, not as an extension or imputation of Jesus’ righteousness (which is what the Protestant doctrine of imputation sometimes holds). In 18.19, he says that the type of body we receive will match the reward or punishment we will face eternally. In 18.20, Cyril indicates that baptism washes away the scars of sins past, and warns against committing sins after baptism, which would not fit with Penal Substitution’s claim to address the juridical penalty of all sins. The idea can fit easily with Medical Substitution, however. Committing a sin damages us, and thus we need to pray, confess, repent, and if necessary be reconciled to others (see lecture 23).