In this work, we use reduced and perturbative models to examine the stability of toroidal Alfven eigenmodes (TAEs) during the internal transport barrier (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. When ion cyclotron resonant heating (ICRH) is used to destabilize TAEs, 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 experiments, and conversely, modes that are predicted to not be driven are not observed. Linear damping rates due to a variety of mechanisms acting during the afterglow are calculated, with important contributions coming from the neutral beam and radiative damping. For DT equivalent extrapolations of discharges without ICRH heating, we find that for the majority of modes, alpha drive is not sufficient to overcome radiative damping.