The dynamics of (few) electrons dissolved in an ionic fluid—as when a small amount of metal is added to a solution while upholding its electronic insulation—manifests interesting properties that can be ascribed to nontrivial topological features of particle transport (e.g., Thouless' pumps). In the adiabatic regime, the charge distribution and the dynamics of these dissolved electrons are uniquely determined by the nuclear configuration. Yet, their localization into effective potential wells and their diffusivity are dictated by how the self-interaction is modeled. In this article, we investigate the role of self-interaction in the description of localization and transport properties of dissolved electrons in non-stoichiometric molten salts. Although the account for the exact (Fock) exchange strongly localizes the dissolved electrons, decreasing their tunneling probability and diffusivity, we show that the dynamics of the ions and of the dissolved electrons are largely uncorrelated, irrespective of the degree to which the electron self-interaction is treated, and in accordance with topological arguments. This record contains input and analysis scripts to reproduce the findings of this article.