Spinodal decomposition of ternary semiconductor alloys during lattice-matched heteroepitaxy is considered here. It has been previously demonstrated that a perfectly flat surface (with no step) would forbid alloy demixing. The case of a rough surface is the purpose of this article. How the possibility of a better strain relaxation introduced by the surface roughness can favor alloy demixing is analyzed first. The present results are exemplified by the AlInAs lattice matched to the InP case. Second, a step-by-step model is proposed to simulate the growth process on a rough surface. This model leads to a description of the strain and alloy demixing during this growth. This study clearly shows how and why the atoms corresponding to binary materials with lower surface tension naturally tend to segregate towards bumped areas.