Colloidal crystals are often prepared by evaporation from solution, and there is considerable interest to link the processing conditions to the crystal morphology and quality. Here, we study the evaporation-induced assembly of colloidal crystals using massive-scale nonequilibrium molecular dynamics simulations. We apply a recently developed machine-learning technique to characterize the assembling crystal structures with unprecedented microscopic detail. In agreement with previous experiments and simulations, faster evaporation rates lead to earlier onset of crystallization and more disordered surface structures. Surprisingly, we find that collective rearrangements of the bulk crystal during later stages of drying reduce the influence of the initial surface structure, and the final morphology is essentially independent of the evaporation rate. Our structural analysis reveals that the crystallization process is well-described by two time scales, the film drying time and the crystal growth time, with the latter having an unexpected dependence on the evaporation rate due to equilibrium thermodynamic effects at high colloid concentrations. These two time scales may be leveraged to control the relative influence of equilibrium and nonequilibrium growth mechanisms, suggesting a route to rapidly process colloidal crystals while also removing defects. Our analysis additionally reveals that solvent-mediated interactions play a critical role in the crystallization kinetics and that commonly used implicit-solvent models do not faithfully resolve nonequilibrium processes such as drying.