This post will be a sort of work in progress for me as I think through my position on Revelation 20 in relation to the two deaths and the two resurrections. My position might easily change, but this is what I currently think. I have found, through emailing Dr. Fowler White, that this is the Augustinian position. My understanding of it has definitely been shaped by Dr. White’s own work.
There are two deaths. The first death is the death of the body, and the second death is the death of the soul while both body and soul are in agony in Hell (this needs to be qualified by the fact that the unbeliever’s soul is always dead throughout life, death, and the resurrection of the body). There are two resurrections. The first resurrection is of the soul (this is identical to regeneration, which Paul describes in Ephesians 2 with resurrection language), the second resurrection is of the body, reuniting the body with the soul (though not automatically specifying which eternal destiny results).
The first death (of the body) that Adam and Eve brought upon themselves in the Garden of Eden established a link to the second death, in addition to securing the perpetual death of the unbelievers’ souls. For natural unsaved humanity, the first death leads to the second death. That link is what Christ came to break. Jesus simultaneously established a link between the first and second resurrection while breaking the link between the first and the second death. This new link is a guaranteed link, and it guarantees two things: it guarantees the second resurrection and, even more importantly, freedom from the second death (this is what Revelation 20:6 is talking about, according to Augustine). At the second resurrection, of course, believers are freed from the first death as well. So the first resurrection frees us directly from the second death and, through its guarantee of the second resurrection, frees us indirectly from the first death.
Lastly (and this is most directly influenced by Dr. White’s work), both resurrections have a certain irony to them. The first resurrection has this irony for the believer: it does not free him from experiencing the first death. It promises eventual emancipation, but not immediate freedom. The second resurrection has a mirror image irony: it does not free the unbeliever from the second death.