In this paper we derive the expansion of the generalized domain-wall fermion Dirac operator including electromagnetic corrections up to $𝒪(e^2)$, which are relevant for lattice computations of radiative corrections to hadronic processes with chiral fermions. In the generalized formulation of the domain-wall fermionic QCD+QED action, physical quark fields are related to the corresponding five-dimensional fields in a way which depends on the (QCD+QED) gauge links, generating extra contact terms when expanding correlation functions with respect to the electric charge. We re-derive the known first-order correction using a background-field approach and, at second order, obtain new local operator insertions (seagull vertices) required for gauge covariant calculations.