Neither EA-CIS nor EA-TDDFT explicitly encode double excitations into the wave function. Instead, nearly all of the orbital relaxation in the resultant spectra comes from the self-consistent optimization of the core-ionized reference orbitals. In this sense, the only difference between EA-CIS and CIS is the reference state while EA-TDDFT includes an additional correction for particlehole self-interaction error relative to TDDFT. Any differences in the qualitative nature of the electron-affinity-based spectra and those of standard linear response theories can therefore be attributed to the difference in the reference orbitals (i.e. orbital relaxation) in the case of CIS/EA-CIS along with an additional (roughly linear) correction to the excitation energies in the case of TDDFT/EA-TDDFT.