Joseph Smith made a couple of editorial changes here in 𝓟 at this transition in the narrative. First, he deleted “it came to pass that”; and second, he replaced the pronoun he with Alma in order to prevent any possible misinterpretation of who the text was referring to. In other words, Joseph Smith’s intended text was “and after Alma had made an end of speaking unto the people / many of them did believe on his words”. For some reason, Joseph’s changes were not implemented in the 1837 edition. Perhaps they were just missed, or perhaps it was decided that these changes were not crucial. However, the conjunction that at the end of “it came to pass” was omitted in the 1837 edition, perhaps unintentionally. The critical text will, of course, restore the original that here in Alma 14:1. For further discussion regarding that after “it came to pass”, see under 2 Nephi 1:1 as well as more generally under that in volume 3.
Summary: Restore in Alma 14:1 the that which was omitted after “it came to pass” in the 1837 edition.