In the printed editions, this passage contains five occurrences of the subordinate conjunction that;
three of these are related to the initial “it came to pass” clause:
Normally, such that’s are repeated only once. And in fact, in the earliest text the first that is lacking; that is, the that immediately following “it came to pass” is secondary and was added by the 1830 typesetter. When Oliver Cowdery wrote down this passage in 𝓞, he supralinearly supplied the repeated that (the one that comes after the when-clause). There is no change in the level of ink flow for the supralinear that itself, although the insert mark was written with heavier ink flow. The critical text will restore the earliest reading here in Alma 58:14, where there is a that both right before and after the long when-clause but not immediately after “it came to pass”.
Elsewhere in the text, we have the following cases of “it came to pass (that) on the morrow (that) S”, where S is a finite clause:
In the last example (Ether 15:17), spacing between surviving fragments suggests that 𝓞 may have had, at least initially, the repeated that (that is, 𝓞 may have read “it came to pass that on the morrow that they did go again to battle”). The second of these that ’s was either crossed out in 𝓞 or was accidentally dropped when Oliver Cowdery copied the text into 𝓟. The textually correct solution will be to follow the earliest extant reading (namely, the reading of 𝓟, without the repeated that).
Including the example from Alma 58:14, we get the following statistics in the earliest text for the construction “it came to pass (that) on the morrow (that) S”:
Joseph Smith’s editing changed the one original example, in Jacob 7:17, of the repeated that (designated above as that ... that) to an example of the most frequent case (that ... NULL). Of course, here in Alma 58:14, the 1830 typesetter created an example of the infrequent repeated that. There is considerable variation, so in each case the critical text will follow the evidence from the earliest extant text. For a complete discussion of the repeated subordinate conjunction that, see under that in volume 3. For another case of the repeated that, see nearby under Alma 58:26.
Summary: Remove in Alma 58:14 the intrusive that added by the 1830 typesetter, thus restoring the earliest text as well as indirectly removing one of the repeated that ’s in this passage (giving “it came to pass on the morrow that when the Lamanites saw …”).