The earlier-described master equation approach to configurational kinetics of non-equilibrium alloys is applied to study L1₂-type orderings in FCC alloys. We describe the kinetic tetrahedron cluster-field method which generalizes a similar method used for equilibrium systems to the case of non-equilibrium alloys. The method developed is used to simulate A1 L1₂ and A1 A1+L1₂ transformations after a quench of an alloy from the disordered A1 phase to the single-phase L1₂ state or the two-phase A1+L1₂ state for a number of alloy models with both short-range and long-range interactions. Simulations of the A1 L1₂ transition show a sharp dependence of the microstructural evolution on the type of interaction, and particularly on the interaction range. The simulations also reveal a number of peculiar features in both the transient microstructures and the transformation kinetics, many of them agreeing well with experimental observations. Microstructural evolution under A1 A1+L1₂ transition was found to be less sensitive to the type of the finite-range (`chemical') interaction, while in the presence of elastic interaction this evolution shows a number of specific features which were earlier discussed phenomenologically by Khachaturyan and co-workers and are illustrated by our simulations. We also consider the problem of the occurrence of a transient congruent ordering under A1 A1+L1₂ transformation and discuss the microstructural features of this stage.