Here we have an example of the subordinate conjunction after being followed by that. As in the case of because that (see 1 Nephi 1:14), Joseph Smith usually deleted the archaic use of that in his editing for the 1837 edition. (One example where he did not delete the that is in 3 Nephi 12:1: “and after that ye are baptized with water / behold I will baptize you with fire and with the Holy Ghost”.) The critical text will, of course, restore all cases of after that whenever the earliest textual sources support the archaic use of the that. For a complete discussion of both the edited and unedited examples, as well as ones without the that, see subordinate conjunctions in volume 3.
Just like because that, we find examples of after that in the King James Bible:
Summary: Follow the earliest textual sources in determining whether subordinate conjunctions like after should be followed by that.