Rhetorical: Alma now moves very clearly away from the physical and into the spiritual. Alma does so by mixing his language with possible references to the past and language that at least a modern audience recognizes as eschatological language. When Alma asks "were the bands of death broken?" what does he mean?
It is possible that there were some who had died, but since this is still prior to the first resurrection, this should not have the meaning that we typically ascribe to those words. In the context of his story, Alma is referring to the fact that the peoples escaped without great loss of life. This is a return to the theme of God's miraculous deliverance. If the deliverance from death was literal, what about the "chains of hell?" In Alma's sermon, the religious ideas were as dangerous as the physical bondage, and it is probable that it is these competing religious ideas that are equivalent to the "chains of hell." When Alma the Elder's people lived under the reign of King Noah, they would have been followers (if not believers) in that other religion. That religion would, in the afterlife, lead to the chains of hell because it was powerless to save. Thus the two conditions of Alma the Elder's people are here repeated in a slightly different format. They were under physical and spiritual danger. From both of those they were saved.
Of course the concept of being saved has a dual meaning as well. They were temporally saved because they were physically delivered from the dangerous conditions. They were spiritually saved because they were able to find the truth in the church, and through that truth (and particularly the belief in the Atoning Messiah) they were spiritually saved.