How does reformed theology reconcile the universal resurrection with limited atonement

The Reformed understanding of the wages of sin being death is that the preeminent death we suffer is not physical, but rather spiritual. In Genesis 2:17, Adam was told "you must not eat from the tree of the knowledge of good and evil, for when you eat from it you will certainly die." Yet when he ate of it, he did not immediately physically die. In the New Testament, several passages explain this more clearly.

For as the Father raises the dead and gives them life, so also the Son gives life to whom he will. For the Father judges no one, but has given all judgment to the Son, that all may honor the Son, just as they honor the Father. Whoever does not honor the Son does not honor the Father who sent him. Truly, truly, I say to you, whoever hears my word and believes him who sent me has eternal life. He does not come into judgment, but has passed from death to life.

• John 5:21-24

Here we see that those who hear and believe have passed from death to life (even while their bodies are still alive).

Do you not know that all of us who have been baptized into Christ Jesus were baptized into his death? We were buried therefore with him by baptism into death, in order that, just as Christ was raised from the dead by the glory of the Father, we too might walk in newness of life. For if we have been united with him in a death like his, we shall certainly be united with him in a resurrection like his.

• Romans 6:3-5

We are united with Christ through baptism into his burial, and just as he was physically resurrected, so too are we able to walk in newness of life (presently, not just after the physical resurrection).

Now if Christ is proclaimed as raised from the dead, how can some of you say that there is no resurrection of the dead? But if there is no resurrection of the dead, then not even Christ has been raised. And if Christ has not been raised, then our preaching is in vain and your faith is in vain. We are even found to be misrepresenting God, because we testified about God that he raised Christ, whom he did not raise if it is true that the dead are not raised. For if the dead are not raised, not even Christ has been raised. And if Christ has not been raised, your faith is futile and you are still in your sins.

• 1 Corinthians 15:12-17

Christ's physical resurrection is not just a promise for us of our future physical resurrection, but an acknowledgement of the power of Christ to take us out of the death of sin into the newness of life in Christ. If Christ was not resurrected, we are still in our sins because that would mean Christ cannot defeat spiritual death. Spiritual life means we are no longer in our sins.

And you were dead in the trespasses and sins in which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience— among whom we all once lived in the passions of our flesh, carrying out the desires of the body and the mind, and were by nature children of wrath, like the rest of mankind.

• Ephesians 2:1-3

Here it is very clear; we were once dead. In what sense? It cannot be physical death, so it must be spiritual death.

For this is why the gospel was preached even to those who are dead, that though judged in the flesh the way people are, they might live in the spirit the way God does.

• 1 Peter 4:6

The gospel is preached to those who are dead, not physically (or how could they hear it?) but to those who are spiritually dead, and might live in the spirit (that is, become spiritually alive).

So when people are physically resurrected, this doesn't mean they have been spiritually made alive. They are still spiritually dead, which is far more important than physical death. In addition, there is a sense in which the lake of fire is a perpetual state of physical death in some way, but I don't think that's particularly pertinent. The punishment of sin is primarily spiritual death, not physical death.