Controlling ultrafast material transformations with atomic precision is essential for future nanotechnology. Pulsed laser annealing (LA), inducing extremely rapid and localized phase transitions, is a powerful way to achieve this but requires careful optimization together with the appropriate system design. We present a multiscale LA computational framework that can simulate atom-by-atom the highly out-of-equilibrium kinetics of a material as it interacts with the laser, including effects of structural disorder. By seamlessly coupling a macroscale continuum solver to a nanoscale superlattice kinetic Monte Carlo code, this method overcomes the limits of state-of-the-art continuum-based tools. We exploit it to investigate nontrivial changes in composition, morphology, and quality of laser-annealed SiGe alloys. Validations against experiments and phase-field simulations as well as advanced applications to strained, defected, nanostructured, and confined SiGe are presented, highlighting the importance of a multiscale atomistic-continuum approach. Current applicability and potential generalization routes are finally discussed.