We study a nonlinear coupled parabolic system with non-local drift modelling inter-species interactions in a ternary mixture with evaporation. We establish well-posedness and develop a convergent, stable finite-volume scheme to approximate weak solutions. Numerical simulations in 2D and 3D investigate how evaporation affects phase-separation morphologies, comparing the continuum model with its underlying stochastic particle system. While simulations are successful without evaporation in both dimensions, activating evaporation introduces new challenges in 3D. We conclude by highlighting open mathematical questions arising from this framework.