An account is given of structure in the prominent vibronic transitions within the ⁴A_2g to ²E_g absorption and emission bands of Mn⁴⁺ in Cs₂SiF₆. The emission lines associated with the nu ₃(t_1u), nu ₄(t_1u) and nu ₆(t_2u) vibrations of the MnF₆^2- octahedron all give symmetrical line shapes. On the other hand, the high resolution absorption spectrum reveals that the lines associated with the nu ₃(t_1u) and nu ₆(t_2u) vibrations are composed of two and four lines respectively with overall separations of approximately 5 cm^-1. Low-temperature, high-field Zeeman measurements are used to show that this structure arises from the splitting of the vibronic levels due to the electron-odd-vibration interaction. For both cases a very good account of the splittings and the intensities including the Zeeman measurements are given in terms of two vibronic coupling and two intensity parameters. This is the first time a vibronic splitting associated with a Gamma ₈ electronic state has been conclusively demonstrated.