We can readily understand that when the afflictions became great Alma's people turned to God.
Indeed, it is one of the sad facts of many lives that only dire afflictions will remind them of their need for God's aid. However, for this people, it is not a return to God, but a new call for deliverance. This was already a righteous people. This mighty cry was not one of a people humbled to submission to God (as was Limhi's people) but rather a righteous people who are responding to extremeties.
What is interesting here is the idea that they "began to cry mightily to God." The interest is not in the "cry" but in the "began." Surely this was a people already familiar with God and with daily supplication to God. What requires the use of "began?"
I suggest that the original tribute status was accepted and acceptable to the people of Alma. It was when Amulon increased the burdens upon them that they "began to cry."
Thus the original "deal" would have been acceptable, but it is this increased persecution that has pushed them to the limits of their abilities. Of course in this increased persecution they would increasingly turn to God for relief, as they could find none from their own powers.