The evidence of his conversion is that he desires to share the taste of heaven that he has received with others. As noted above, the cleansing from sin was an instantaneous event, but the actual process of living the gospel; of finishing the repentance process, required something more. What he now does is to attempt to undo the damage he had done. He had led them away, now he will attempt to lead them back.
While Alma is clearly discussing his own experience, he tells it to Helaman for a reason. The first would be to simply provide background, but since Helaman was his son, it is quite likely that it was a story with which Helaman was familiar. The other reason is that the story itself is meant to be instructive. It is instructive not in the spectacular nature, which we do not hope (or fear) to endure, but in the general process by which we must be reconciled to God. We are found in a sinful state. It is essential that we follow Alma’s pattern, and recognize our state with true remorse sufficient to effect a change in our natures. We must call upon Christ, and accept his atoning sacrifice, and then be filled with the Holy Ghost. Lastly, we must implement that experience in our lives for the benefit not only of ourselves, but of others.