We theoretically study the impact of solvent evaporation on the dynamics of isothermal phase separation of ternary polymer solutions in thin films. In the early stages we obtain a spinodal length scale that decreases with time under the influence of ongoing evaporation. After that rapid demixing occurs at a well-defined lag time, a morphology emerges of which the compositions of the coexisting phases rapidly approach the binodal values. We find that the type of morphology, which can be either bicontinuous or dispersed, strongly depends on the evaporation rate if the solubility of the two solutes in the common solvent differs. We derive expressions that relate both the lag time and length scale characterizing the emerging morphology to all relevant physical parameters. These include the tracer diffusivities, the interaction parameters, the degrees of polymerization, the blend composition, and the evaporation rate. In agreement with our numerical results, we find the latter to scale with a one-sixth power of the evaporation rate. Following the lag time, a new length scale appears that increases with time due to coarsening. If evaporation is sufficiently slow, this length increases with the conventional one-third power of time. For rapid evaporation deviations from that may occur, especially if the solvent compatibility of the solutes differ. Our model calculations suggest that the characteristic features of the final dry-film morphology is dictated by the quench depth as well as the time available for coarsening, which are both determined by the rate of evaporation.