According to Rodney Turner, the joint baptism of Alma and Helam is without precedent in all scripture. Alma must have felt impressed to share in the first baptism and thereby set the example for all who were to follow. There is no other account of Alma's being baptized. The baptisms performed by Alma are the first recorded in the Book of Mormon. [Rodney Turner, "Two Prophets: Abinadi and Alma," in Studies in Scripture: Book of Mormon, Part 1, pp. 258-259]
“Both Alma and Helam Were Buried in the Water”
When "both Alma and Helam were buried in the water" (Mosiah 18:14), was Alma baptizing himself for the first time? And where did he get his authority? According to McConkie and Millet, there is no question but that Alma held the priesthood (see commentary on Mosiah 18:18), and that he was ordained after the holy order of God. Thus he would have been baptized previously. "Therefore, when Alma baptized himself with Helam that was not a case of Alma baptizing himself, but merely as a token to the Lord of his humility and full repentance." (Joseph Fielding Smith, Answers to Gospel Questions, 3:203-4) [Joseph F. McConkie and Robert L. Millet, Doctrinal Commentary on the Book of Mormon, Vol. II, p. 258]
“Both Alma and Helam Were Buried in the Water”
In Mosiah 18:14 it says that after Alma had pronounced a covenant prayer of baptism, "both Alma and Helaman were buried in the water; and they arose and came forth out of the water rejoicing, being filled with the Spirit. And again; Alma took another and went forth a second time into the water, and baptized him according to the first, only he did not bury himself again in the water."
Question: Where did Alma get his authority? And, Was Alma baptizing himself at this time?
According to Joseph Fielding Smith, we may conclude that Alma held the priesthood before he, with others, became disturbed with King Noah. . . . If he had authority to baptize that is evidence that he had been baptized. Therefore, when Alma baptized himself with Helam that was not a case of Alma baptizing himself, but merely as a token to the Lord of his humility and full repentance. . . . If I remember correctly, there is no reference to the baptism of Alma the elder or Helaman nor of Nephi and his brother Jacob, but we know they were baptized as were all the faithful members in the Church. [Joseph Fielding Smith, Answers to Gospel Questions, Vol. 3, pp. 203-204]