Alma's answer to Zoram contains information that is instructive for the real world in which the Nephites lived. The first question that we can answer with this information is the specific path of the Lamanites. They were north of Zarahemla, or downstream from Zarahemla. They must have retreated to the wilderness from which they had come in order to miss the Nephite cities on the west which would have created a problem for their retreat with captives. Thus we may expect that they traveled south through the west wilderness.
When Alma tells Zoram that they would be crossing the Sidom south near Manti, we find them exiting Nephite territory through the more time honored passage between the land of Nephi and the land of Zarahemla. Thus we may suggest that the way through the wilderness was a relatively difficult passage, and when laden with captives, and do doubt booty, the Lamanites opted for the easier route home.
The next issue that is answered for us is how the Nephites who were unable to respond quickly enough to save Ammonihah could still intercept the Lamanite army that had a clear time advantage over the Nephite armies. The Lamanite army was northwest of Zarahemla, and had to travel to south of Zarahemla in order to exit by the pass noted. Thus the army had to travel toward and past the stronghold or Zarahemla. Even though the Nephite army was unable to make the trip north to Ammonihah in time, they did have time to head the shorter distance south. Knowing where the Lamanite army would be further decreased the required travel time, allowing for the intercept near Manti.