JOEL - We have of course been instructed by Jesus Himself that we should pray to Heavenly Father.

"After this manner therefore pray ye: Our Father which art in heaven, Hallowed be thy name." (Matt. 6:9, Luke 11:2, 3 Ne. 13: 9)

So I don't know why some members seem to pray to Jesus; perhaps its a leftover habit from before they were members.

Here are the Alma scriptures in question:
"And it came to pass that as I was thus racked with torment, while I was harrowed up by the memory of my many sins, behold, I remembered also to have heard my father prophesy unto the people concerning the coming of one Jesus Christ, a Son of God, to atone for the sins of the world. Now, as my mind caught hold upon this thought, I cried within my heart: O Jesus, thou Son of God, have mercy on me, who am in the gall of bitterness, and am encircled about by the everlasting chains of death." (Alma 36:17-18)

In these scriptures Alma the younger is telling his son, Helaman, about his conversion from being an enemy of God and His Church to receiving forgiveness of his sins and converting to the ways of God(Mosiah 27). Technically I would not really call this a prayer. Because of his wicked past, he didn't know much about God and Jesus nor the proper way to pray. And at his moment of great torment, because of the recognition of his own sins, he suddenly understood his father's past teachings about Jesus Christ who would atone for the sins of the world. Remembering this he desperately cried within his heart to this Jesus to have mercy on him.
By the way, for those who don't know better, it is not really a sin to talk to Jesus, if one feels so inclined; it's just that we have been taught that we should pray to our Heavenly Father in the name of Jesus Christ. The entire Godhead is involved in the answers to our prayers.