Studies of plasma injection signatures at the giant planets commonly interpret these events in terms of a longitudinally localised ‘bundle’ of hot plasma or a more radially-extended flow channel. In either picture, the hotter plasma moves radially inward toward the planet and gains energy. These structures also entrain energetic charged particles. These charged particles have important azimuthal secondary drifts, eventually removing them from the injection location at different, energy-dependent velocities, leading to the ‘dispersed’ signature in observed energy spectra. In this study, we revisit the modelling of azimuthal gradient and curvature drift rates for injected particles, using a magnetodisc field rather than the pure dipole which is often assumed. We comment on the quantitative effect of the magnetodisc field on the energy dispersion of older injection events at Saturn where simultaneous multiple energy bands are observed in Cassini LEMMS proton data.