Energy shifts in time dependent perturbation theory

[Malamala]

Hello! I saw in many papers people talking about the effects of a time dependent perturbation (usually an oscillating E or B field) on the energy levels of an atom or molecule (for now let's assume this is a 2 level system). Taking about energy makes sense when the hamiltonian is time independent. But here it is not. Moreover, this shift (e.g. AC Stark Shift) it's a constant (which depends on the magnitude and frequency of the field), even if the field itself is time varying. Given that this is usually talked about in the context of perturbation theory, I assume that at a point we do an approximation related to the relative frequencies of the field and of the atom (the resonance frequency), but I am not sure how to proceed. Can someone help me a bit in understanding this? Here is the paper that I am reading that made me ask this question. Thank you!