Here the original text has an example of the repeated that: “and it came to pass that when Alma had said these words that Zeezrom leaped upon his feet”. Initially in 𝓟, as Oliver Cowdery copied from 𝓞, he omitted the repeated that. Shortly thereafter, he supralinearly inserted the that (there is no difference in the level of ink flow). Most probably, 𝓞 had the repeated that.
When Joseph Smith removed the instance of “it came to pass that” in his editing of this passage for the 1837 edition, he also removed the repeated that (as one would expect). For further discussion of the occasional elimination of the phrase “come to pass” in the 1837 edition, see under 1 Nephi 10:17 (also see under come to pass in volume 3). The use of the repeated that is quite frequent in the original text, although many instances (but not all) were removed by Joseph in his editing for the 1837 edition; for example, the repeated that was left in Mosiah 9:11: “therefore it came to pass that after we had dwelt in the land for the space of twelve years that king Laman began to grow uneasy”. For discussion of the repeated that, see under 1 Nephi 10:2–3 as well as more generally under that in volume 3.
Summary: Restore in Alma 15:11 the original “it came to pass that” and the repeated that after the subordinate clause: “and it came to pass that when Alma had said these words that Zeezrom leaped upon his feet”.