The question here is whether after that is a prepositional phrase or the archaic conjunctive construction after that (which is equivalent to simply after in modern English). The 1830 typesetter interpreted the that here as a pronoun since he placed a comma after it. In this instance, if we delete the that, we get a sentence fragment, which means that the 1830 typesetter’s decision was very likely correct.
The intended meaning of this passage is that the Lamanite armies first destroyed the people in the land of Ammonihah; then there were many battles with the Nephites, the result of which was a major defeat for the Lamanites, which included the destruction of almost all the Amulonites (who had joined the Lamanites). The pronominal that and its accompanying comma should therefore be retained here in the standard text for Alma 25:3. For further discussion of the possible ambiguity of after that in the text, see under Alma 5:5.
Summary: Maintain in the standard text the comma after the prepositional phrase after that in Alma 25:3; here the that is a pronoun, not the conjunctive that which typically follows the subordinate conjunction after in the Book of Mormon text.