The first resurrection as mentioned in Revelation is not the rapture.
If you'll notice, there is no translation of the living mentioned in the first resurrection. That's because the rapture and the first resurrection of Revelation are two separate events.
There is a second resurrection those who will suffer the second death.
Only those who died and resurrected in the first, are saved.
Revelation 20:5-6 New International Version (NIV)
(The rest of the dead did not come to life until the thousand years were ended.)
This is the first resurrection. Blessed and holy are those who share in the first resurrection. The second death has no power over them, but they will be priests of God and of Christ and will reign with him for a thousand years.
Those who died in Christ will share the first resurrection when the Lord Jesus Christ comes to save his people, his church, his body. Of course those who are alive on the second advent of Christ, will be saved as the Bible says:
1 Thessalonians 4:13-17 New International Version (NIV)
Brothers and sisters, we do not want you to be uninformed about those who sleep in death, so that you do not grieve like the rest of mankind, who have no hope. For we believe that Jesus died and rose again, and so we believe that God will bring with Jesus those who have fallen asleep in him. According to the Lord’s word, we tell you that we who are still alive, who are left until the coming of the Lord, will certainly not precede those who have fallen asleep. For the Lord himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God, and the dead in Christ will rise first. After that,
we who are still alive and are left will be caught up together with them in the clouds to meet the Lord in the air. And so we will be with the Lord forever.
1 Corinthians 15:50-52 New International Version (NIV)
I declare to you, brothers and sisters, that flesh and blood cannot inherit the kingdom of God, nor does the perishable inherit the imperishable. Listen, I tell you a mystery:
We will not all sleep, but we will all be changed— in a flash, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, the dead will be raised imperishable, and we will be changed.
When the Lord Jesus returns, he will save his sheep who died [fallen asleep] and who are alive.