D&C 19 has a really interesting explanation of the meaning of eternal that may also apply to its usage in Alma:
4 And surely every man must repent or suffer, for I, God, am endless.
5 Wherefore, I revoke not the judgments which I shall pass, but woes shall go forth, weeping, wailing and gnashing of teeth, yea, to those who are found on my left hand.
6 Nevertheless, it is not written that there shall be no end to this torment, but it is written endless torment.
7 Again, it is written eternal damnation; wherefore it is more express than other scriptures, that it might work upon the hearts of the children of men, altogether for my name’s glory.
8 Wherefore, I will explain unto you this mystery, for it is meet unto you to know even as mine apostles.
9 I speak unto you that are chosen in this thing, even as one, that you may enter into my rest.
10 For, behold, the mystery of godliness, how great is it! For, behold, I am endless, and the punishment which is given from my hand is endless punishment, for Endless is my name. Wherefore—
11 Eternal punishment is God’s punishment.
12 Endless punishment is God’s punishment.
In other words, as I understand these verses, eternal punishment does not mean a punishment that has no end, but punishment that is dealt out by God. Eternal is "more express" "that it might work upon the hearts of the children of men" for God's glory (v. 7).