In this work, we use reduced and perturbative models to examine the stability of TAEs during the ITB afterglow in JET experiments designed for the observation of alpha driven TAEs. We demonstrate that in JET-like conditions, it is sufficient to use an incompressible cold plasma model for the TAE to reproduce the experimental adiabatic features such as frequency and position. The core-localised modes that are predicted to be most strongly driven by minority ICRH fast ions correspond to the modes observed in the DD experiment, and conversely, modes that are predicted to not be driven are not observed. Various linear damping mechanisms are calculated during the afterglow, and Landau damping by the thermal plasma is shown to be clearly dominant for observed modes. We show that analytical estimates for Landau damping can be wrong by an order of magnitude in these experiments, owing to the neglect of the higher order sideband resonances. For DT equivalent extrapolations, we conclude that a different set of TAEs that exist towards the edge are more likely to be driven unstable than the DD observed core modes.