The fine structure of the "excited-electron" trion triplet state in negatively charged CdSe/ZnSe self-assembled quantum dots is studied using polarization-selective as well as magneto-photoluminescence spectroscopy on a single-dot level. The charged biexciton emission where the optically active triplet states with total angular momentum projections ±1/2 and ±3/2 are left behind is used as a monitor. The line separation provides an energy of Δ ₀=1.5 meV for the isotropic electron-hole exchange interaction. The anisotropic electron-hole exchange creates a mixing between ±1/2 and ±3/2 triplet states resulting in partially linear polarization as well as specific g factors of the optical transitions. Studying experimentally both types of manifestations, we find a ratio between the anisotropic and isotropic part of Δ ₁/Δ ₀ ≈ 0.5, distinctly larger than for the exciton in uncharged quantum dots. This is caused by the fact that the electron participating in the exchange is in an excited state enhancing the anisotropy.