The expulsion of runaway electrons (REs) during different types of tokamak instabilities is analysed by means of a Cherenkov probe inserted into the scrape-off layer of the FTU tokamak. One such type of instability, the well-known tearing mode, is involved in disruptive plasma termination events, during which the risk of RE avalanche multiplication is highest. The second type, known as anomalous Doppler instability, influences RE dynamics by enhancing pitch angle scattering. Three scenarios are analysed here, characterised by different RE generation rates and mechanisms. The main conclusions are drawn from correlations between the Cherenkov probe and other diagnostics. In particular, the Cherenkov probe permits the detection of fast electron expulsion with a high level of detail, presenting peaks with 100% signal contrast during tearing mode growth and rotation, and sub-peak structures reflecting the interplay between the magnetic island formed by the tearing mode, RE diffusion during island rotation and the geometry of obstacles in the vessel. Correlations between the Cherenkov signal, hard x-ray emission and electron cyclotron emission reveal the impulsive development of the anomalous Doppler instability with instability rise time in the microsecond scale resolved by the high time-resolution of the Cherenkov probe.