What does "God is just" mean according to Calvinists?

Calvinists believe that all who are outside of Christ are condemned under the Covenant of Works. Because God righteously requires perfect perpetual faithful obedience, violators of that law are rightly subjected to punishment. The only hope is to be saved under the Covenant of Grace, where Jesus dies as a substitute and the sinner is saved by faith-union to him through the Holy Spirit.

For the case of reprobates, while all will be condemned, their punishments are not equal. Greater sins carry greater punishments, both presently and eternally. Nevertheless, Calvinists generally have little occasion to talk about this because to die outside of Christ already entails a severe punishment on the grounds of the violated Covenant of Works and the scorning of the savior. The solution for sinners of very heinous crimes is the same as the solution for sinners of less heinous crime: repent and believe in the Lord Jesus, grow in faith and sanctification for your life after that.

While he affirmed God's justice as having real meaning, John Calvin attributed to it a hiddenness that renders it opaque to humans. On reprobation (Institutes 3.21.5–3.23.9):

We must always at last return to the sole decision of God's will, the cause of which is hidden in him…. For if predestination is nothing but the meting out of divine justice—secret, indeed, but blameless—because it is certain that they were not unworthy to be predestined to this condition, it is equally certain that the destruction they undergo by predestination is also most just…. The reprobate wish to be considered excusable in sinning, on the ground that they cannot avoid the necessity of sinning, especially since this sort of necessity is cast upon them by God’s ordaining. But we deny that they are duly excused, because the ordinance of God, by which they complain that they are destined to destruction, has its own equity—unknown, indeed, to us but very sure.

Even more radically, Calvin separated God's decretive will (Providence, what God actually does) from His revealed will (the Law, what He tells people to do) so much that the meaning of "justice" does not truly correspond between the two. And Calvin places priority on the former as representing God's true character. Commenting on Job 4:18, Calvin actually argued that God could in His justice condemn even unfallen angels:

But there is another kind of justice which is most strange to us; namely, if God were not to treat us according the Law but according as He can justly act. The Law is not so perfect or exquisite as is that infinite justice of God…according to which he could find iniquity in his angels and the sun would be unclean before him. See, then, how there is a justice more perfect than the Law. If one accomplished everything in the Law, he could still be condemned if God wanted to use this justice. True, the Lord does not wish to use it since he accommodates himself to us and receives and accepts that justice which he has commanded.

You are correct in noting that in Calvinism one's ultimate eschatological end is the result of either God electing one to glory or one to destruction.

However, because Calvinist care about what Scripture teaches, they also hold to the belief that their are varying degrees of punishment (and supposedly varying degrees of glory) rendered individually to each man.

Here are a few obvious passages which strongly suggest gradations of punishment in hell.

[God] will render to every man according to his works. (Romans 2:6)

[This is the conclusion of one of Jesus' parables.] The servant who knows the master's will and does not get ready or does not do what the master wants will be beaten with many blows. But the one who does not know and does things deserving punishment will be beaten with few blows. From everyone who has been given much, much will be demanded; and from the one who has been entrusted with much, much more will be asked. (Luke 12:47-48)

One popular Calvinist outlet, Ligonier Ministries, defends this belief with no qualms.

There will be degrees of punishment during the day of wrath. One “trivial” sin makes us guilty of the whole law and liable to eternal torment (James 2:10). Yet some acts are worse than others and deserve harsher punishment (Num. 35:9–29). As bad as Sodom was, her sentence will be lighter on Judgment Day than Bethsaida’s because Sodom never saw Jesus (Matt. 11:20–24). The sinner who never hears of Christ will go to hell, yet his pain will be less intense than those who hear the Gospel each Sunday and refuse to repent.

So then, does the Bible say that, because God is just, both of them will have the same punishment tormented in the lake of fire eternally? The answer is no from a cursory reading of the Bible, and the answer is also no from a normal Calvinistic reading of the Bible.

Though your question seemed to imply that you're wondering what justice means to a Calvinist. I would suggest clarifying exactly what it is that you are asking. For self study on this subject, look into forensic justification and double imputation. Those who fail to have Christ' righteousness imputed to them are left with Adam's sin and their own personal sins left imputed to their own accounts. You ultimately get what's imputed to you, and the more grievous the sin that's imputed to you, the more judgement you receive.

Source: https://www.ligonier.org/learn/devotionals/degrees-punishment/