The question inherently confuses and conflates so many things to begin with.
Eternal life, for example, is not an adverb (i.e. you eternally have life; as opposed to eternal life: life that is undending for those in possession of it), and as such doesn't preclude punishment before being admitted thereto. "Indeed," says St. Paul,
2 Corinthians 5:10 (ESV).. we must all appear before the judgment seat of Christ, so that each one may receive what is due for what he has done in the body, whether good or evil.
Salvation is from eternal damnation, not from suffering. In fact, Scripture makes suffering a prerequisite to receiving eternal life:
Romans 8:17 (ESV) and if [we are] children, then heirs—heirs of God and fellow heirs with Christ, provided we suffer with him in order that we may also be glorified with him.
Luke 9:23 (ESV) And he said to all, “If anyone would come after me, let him deny himself and take up his cross daily and follow me.
Then you distinguished between a punishment and a reprimand for wrongdoing. That is to say, between the genus of punishment and a species of that genus, namely, reprimand—a form of punishment.
Then you implied a parable wherein punishment is describes cannot refer to real punishment, leaving one to wonder: what does real but figurative punishment to be warned against (the moral of the story .. of the parable) look like? Or how could Jesus refer to real punishment in a parable?
Yet we have countless explicit examples where Jesus steps out of the parable and explains in a rather lucid manner, e.g.:
Matthew 18:21:35 (ESV) Then Peter came up and said to him, “Lord, how often will my brother sin against me, and I forgive him? As many as seven times?” 22 Jesus said to him, “I do not say to you seven times, but seventy-seven times.
23 “Therefore the kingdom of heaven may be compared to a king who wished to settle accounts with his servants. 24 When he began to settle, one was brought to him who owed him ten thousand talents. 25 And since he could not pay, his master ordered him to be sold, with his wife and children and all that he had, and payment to be made. 26 So the servant fell on his knees, imploring him, ‘Have patience with me, and I will pay you everything.’ 27 And out of pity for him, the master of that servant released him and forgave him the debt. 28 But when that same servant went out, he found one of his fellow servants who owed him a hundred denarii, and seizing him, he began to choke him, saying, ‘Pay what you owe.’ 29 So his fellow servant fell down and pleaded with him, ‘Have patience with me, and I will pay you.’ 30 He refused and went and put him in prison until he should pay the debt. 31 When his fellow servants saw what had taken place, they were greatly distressed, and they went and reported to their master all that had taken place. 32 Then his master summoned him and said to him, ‘You wicked servant! I forgave you all that debt because you pleaded with me. 33 And should not you have had mercy on your fellow servant, as I had mercy on you?’ 34 And in anger his master delivered him to the jailers, until he should pay all his debt. 35 So also my heavenly Father will do to every one of you, if you do not forgive your brother from your heart.”
Cf. Mt 5:25-26.
Notice again: the wicked servant was himself forgiven, but would not forgive others. Clearly the King is Jesus, per St. Paul, and "his servants" are His people. That is, this one is 'saved,' but he must be punished "until" all is aright again—until all accounts are 'settled.'
You can be forgiven your sins but still be punished:
Revelation 3:19 (ESV) Those whom I love, I reprove and discipline, so be zealous and repent.
1 Corinthians 11:32 (ESV) But when we are judged [i.e. punished] by the Lord, we are disciplined so that we may not be condemned along with the world.
If God forgave you your sins but you didn't receive any bad consequences, you would not be changed as a person—you would be the same person inclined to the same evil. That is to say, your guilt as been forgiven, but you need changed if for no other reason than to no longer be the kind of person that does things which make you guilty.
There is the eternal punishment which every wilful sin merits, but there is also the temporal. For example:
2 Samuel 12: 13-14 (ESV) David said to Nathan, “I have sinned against the Lord.” And Nathan said to David, “The Lord also has put away your sin; you shall not die. 14 Nevertheless, because by this deed you have utterly scorned the Lord, the child who is born to you shall die.”
There is still a sense of justice in which God demands a lesser punishment than the eternal, even though the eternal has been forgiven (Hell for all eternity). Of which this is just one example.
So in summary: No, salvation does not preclude suffering, but rather entails it.