Fermi-Hubbard system with a periodically-modulated interaction has been recently shown to resonantly absorb energy at series of drive frequencies. In the present work, with the help of static perturbation theory, we argue that driving couples to Hubbard bands in a similar fashion as a classical field couples to a two-level atom. The latter, significantly simpler set-up, described by the Rabi model, is known to support resonant rapid energy absorption at virtually the same series of driving frequencies. Our interpretation is also supported by the equivalency between dynamics of the two-site periodically-driven Hubbard and Rabi models. Relying on this insight, we establish that the same Rabi-resonant behavior is displayed also by fermions confined in a harmonic trap with periodically-driven contact interactions. arXiv:1904.05714v2 [cond-mat.str-el]