We address the question of the evolution of a nanostructured system in a metastable state to equilibrium. To this purpose, we use the case study of the transition of an AucorePdshell nanoalloy cluster containing up to about 600 atoms toward the equilibrium Au segregated configuration. We start from a molecular dynamics approach with an embedded atom potential. The way the transition develops at low temperatures is found to be very sensitive to the cluster morphology and the way energy is exchanged with the environment. The transition of icosahedral inverse core-shell Au-Pd clusters is predicted to nucleate locally at the surface contrary to clusters with other morphologies, and starting at lower temperatures compared to them.