A combination of complementary high-energy X-ray diffraction, containerless solidification during electromagnetic levitation and transmission electron microscopy is used to map in situ the phase evolution in a prototype Cu-Zr-Al glass during flash-annealing imposed at a rate ranging from 102 to 103 K s-1 and during cooling from the liquid state. Such a combination of experimental techniques provides hitherto inaccessible insight into the phase-transformation mechanism and its kinetics with high temporal resolution over the entire temperature range of the existence of the supercooled liquid. On flash-annealing, most of the formed phases represent transient (metastable) states - they crystallographically conform to their equilibrium phases but the compositions, revealed by atom probe tomography, are different. It is only the B2 CuZr phase which is represented by its equilibrium composition, and its growth is facilitated by a kinetic mechanism of Al partitioning; Al-rich precipitates of less than 10 nm in a diameter are revealed. In this work, the kinetic and chemical conditions of the high propensity of the glass for the B2 phase formation are formulated, and the multi-technique approach can be applied to map phase transformations in other metallic-glass-forming systems.