The post-solidification reactions that take place behind the growth front in directionally solidified ternary eutectic Al-Ag-Cu alloys have a marked influence on the observed room temperature microstructure, obscuring many aspects of the solidification morphology present at the growth front. Quantifying these solid-state processes is necessary for proper interpretation of ex-situ microstructure as an indicator of growth dynamics and operating point selection. In this study, the directional growth structure and phase compositions are quantified as a function of distance from the growth front to describe microstructural changes that occur during cooling in the solid state. The solubility of Ag in the Al(fcc) phase decreases rapidly below the eutectic point, and the excess Ag is accommodated by growth of the Ag2Al(hcp) phase, mainly by motion of the Al(fcc)-Ag2Al(hcp) interface. These structural changes are quantified, and compared to the coupled morphology at the solidification front. A cellular automaton method is proposed here to mimic either the forward or reverse solid-state changes, providing a means to estimate many features of the directional growth morphology based on sampling the structure at some known distance from the front.