We demonstrate that the population of 20--410 keV electrons observed in Saturn's inner magnetosphere result principally from recent injections. Electrons at these energies appear to survive only up to a few days in the neutral gas cloud emitted by gas jets in Enceladus's southern hemisphere. Ions of similar energies have much shorter lifetimes in the gas cloud because of charge-exchange with the ambient neutrals. We have been able to associate fluxes at different energies and times with a single past injection based on the morphology of electron spectrograms from measurements made by Cassini's Magnetospheric Imaging Instrument (MIMI). Once injected, electrons disperse in longitude but the age of the initial injection and its approximate longitude can be reconstructed. Furthermore, the shape of time-dispersed features argues against rigid corotation of the magnetospheric plasma, or a fraction thereof, and instead favors L-dependent flow shear.