Two things are worthy of note here, namely, the nature of the preaching done by the sons of Mosiah and the depth of the conversions. These two aspects of conversion are inextricably tied. These missionaries did not trifle with the Lamanites; they did not entertain them or seek by sophistry or by manipulation to bring people into the Church.
They preached the gospel. They preached creation, fall, and atonement. They preached faith, repentance, and rebirth. They preached Christ. That is, their message was substantive and sacred, and it was presented by the power of the Holy Ghost.
Thus the listeners were converted to Christ, not to the missionaries or the other members of the Church, as pleasant and sincere and dedicated as those might be. They were converted to Christ, and thus their testimonies and their lives were built upon the only sure foundation (see Helaman 5:12).