We study excitation energy transfer (EET) in a model three-site system with a mixed-quantum classical dynamics method, by focusing on the effect of an underdamped vibration. We construct two types of models where the underdamped vibration mode is included either in the quantum subsystem or in the classical bath. We show that the two models yield practically equivalent results despite the different depictions of the vibration. In particular, both models consistently demonstrate accelerations of population relaxation induced by quasi-resonant vibration. This indicates that intricate features of EET dynamics that have been frequently ascribed to the quantal nature of vibrations, such as vibronic mixing, can be successfully reproduced by using physically equivalent but classically described bath modes. The mechanism behind the observed quantum-classical correspondence is proposed. We also systematically examine how the structure of the spectating continuum phonon modes affects the vibronic resonance and observe that phonon modes with different time scales influence the resonance in different manners.