A segregation model for multiple phase transformations is coupled with thermodynamic equilibrium calculations, including dendritic, peritectic and eutectic reactions. Its predictions are compared with measurements deduced from an electro-magnetic levitation solidification experiment of an aluminum-nickel alloy. Quantitative agreement is found for the cooling curve and the fraction of microstructures, providing a validation of the kinetics of phase transformations. The effects of nucleation undercooling and coupling with thermodynamic equilibrium calculations are discussed.