Liquid/liquid phase transitions are inherent to multicomponent solutions, which often contain a diversity of intermolecular interactions between their molecular constituents. In one such example, a phase transition is observed in liquid/liquid extraction where the nonpolar organic phase separates into two phases under sufficiently high metal and acid extraction by the amphiphilic extractant molecule. This deleterious phenomenon, known as third phase formation, complicates processing and limits efficiency. While empirically well documented, the molecular origin of this phenomenon is not understood. The prevailing conceptualization of the organic phase treats it as a microemulsion where extractant molecules form reverse micelles that contain the extracted aqueous solutes in their polar cores. Yet recent studies indicate that a microemulsion paradigm is insufficient to describe molecular aggregation in some solvent extraction systems, implying that an alternative description of aggregation, and explanation for third phase formation, is needed. In this study, we demonstrate that the formation of a third phase is consistent with crossing the liquid-liquid miscibility gap for a molecular solution rather than a Winsor II to Winsor III transition as presumed in the microemulsion paradigm. This insight is provided by using a graph theoretic methodology, generalizable to other complex multicomponent molecular solutions, to identify the onset of phase splitting. This approach uses connectivity obtained from molecular dynamics simulation to correlate the molecular-scale association of extractants and extracted solutes to the solution phase behavior using percolation theory. The method is applied to investigate a solvent extraction system relevant to ore purification and used nuclear fuel recycling: tri-n-butyl phosphate/uranyl nitrate/water/nitric acid/n-dodecane. In analogy to a molecular solution, immediately preceding the liquid-liquid coexistence curve from the single phase region, the metal-ligand complexes percolate. This demonstrates that describing this solution with microemulsion chemistry is neither applicable nor broadly required to explain third phase formation. Additionally, the method developed herein can predict third phase formation phase boundaries from simulation for this and potentially other solvent extraction systems.