In this paper, we look at four generalizations of the one-dimensional Aubry-Andre-Harper (AAH) model which possess mobility edges. We map out a phase diagram in terms of population imbalance and look at the system size dependence of the steady-state imbalance. We find nonmonotonic behavior of imbalance with the system parameters, which contradicts the idea that the relaxation of an initial imbalance is fixed only by the ratio of the number of extended states to the number of localized states. We propose that there exist dimensionless parameters, which depend on the fraction of single-particle localized states, single-particle extended states, and the mean participation ratio of these states. These ingredients fully control the imbalance in the long time limit and we present numerical evidence of this claim. Among the four models considered, three of them have interesting duality relations and their locations of mobility edges are known. One of the models (next-nearest-neighbor hopping) has no known duality but a mobility edge exists and the model has been experimentally realized. Our findings are an important step forward to understanding nonequilibrium phenomena in a family of interesting models with incommensurate potentials.