The cluster dynamics method is used to model at the atomic scale the kinetics of first order phase transformations. Clusters are embryos of the growing phase. Their formation kinetics from the solid solution are obtained by solving a set of master differential equations. This set is the continuity equation of the cluster size distribution function and is based on inter-cluster solute exchanges. These exchanges, absorption and emission of solute atoms, are controlled by the solute diffusivities and the cluster free energies. The model is applied here to the precipitation of Al-3(Zr, Sc) dispersoids with the Ll(2) structure in Al-rich Zr-Sc solid solutions. Several characteristic features are obtained and discussed: 1) In the ternary alloy, the fast (Sc) diffusing species always controls the nucleation, in contrast to classical thermodynamical descriptions. 2) A Zr-Sc thermodynamic coupling induces heterogeneous nucleation on Zr atoms. 3) A segregation on the dispersoids outer shell of the slow diffusing solute (Zr) occurs during the coarsening stage, slowing down their coarsening rate. Finally, some extensions and prospects of the method are considered.