Equilibrium composition profiles (CPs) of epitaxial alloy quantum dots (QDs) are well established theoretically. However nonequilibrium CPs may occur experimentally. Using an atomistic-strain-model Monte Carlo simulation method, we demonstrate a striking correlation between the nonequilibrium CPs of QDs and the kinetic growth mode: the layer-by-layer growth (LG) and faceted growth (FG) form a core-shell structure having the triangle core of the unstrained and V-shaped core of the strained component, respectively, and both are distinctly different from the equilibrium CP. Comparing simulations with experiments, we infer that the InGaAs dots on GaAs grow by FG, while GeSi dots on Si grow first by LG followed by FG. Our findings suggest a possible method for controlling the CPs of QDs by selecting the growth mode.