Alma specifically tells the people that if they place their trust in God that God would deliver them. This will eventually be true in two different ways.
The first is explicit in verse 29. The Almaites are "delivered" because the Lamanites spare their lives. While they will be under tribute-bondage, just as the Limhites were, they are nevertheless alive.
The second "deliverance" will come later when Alma and his people will escape from Helam and travel to Zarahemla. At that point there is a complete deliverance from the Lamanites. This is the message of the story. As indicated in verses 21-24, the Lord will allow the patience of his people to be tried, but will eventually "deliver" them.
For Mormon, this domination by the Lamanites is not a denial of the righteousness of the people, but a trial of that righteousness. There is no indication on Alma's part that this comes as a punishment for the sins of the people. There is no prophetic text decrying the state of Almaite society and admonishing a return to God. These are people who have already made the commitment to follow God, and from all we are able to know of them, they are faithful to that covenant.
In spite of faithfulness, not as a result of sin, Alma's people have their faith "tried." There is no guarantee that following the gospel will shield us from all problems. Indeed, God at times allows us to be tried by the adversities of life. The key is how we respond to those trials. What we are promised is the same as the promise to the people of Alma, eventual deliverance.
Literary: Mormon turns a parallel phrase here as he emphasizes the position of Alma's people before the Lamanites:
….[they] began to cry unto the Lord that he would soften the hearts of the Lamanites, that they would spare them, and their wives, and their children.
Mosiah 23:29
29 And it came to pass that the Lord did soften the hearts of the Lamanites.
In verse 28 they cry unto the lord to "soften the hearts of the Lamanites." In the next verse the Lord answers their cries: "the Lord did soften the hearts of the Lamanites." This repetition of the substance of the prayer ties the request to the granting of the request. They ask God for a certain type of assistance, and the repetition of the phrase marks the direct affirmative response to that cry for assistance.