The vibration mitigation performance of a conventional tuned mass damper (TMD) system is very sensitive to the fluctuation in tuning of the designed frequency to the natural frequency of the main system. In view of the stochastic characteristics of external loading and the errors of identifying system parameters, a hybrid mass damper (HMD) system with optimal selection on control parameters can enhance the designed performance with the help of a supplementary active force acted between the main system and the mass damper. However, the control performance degradation induced by the control force application time delay should be considered and investigated before practical application. Having the best versatility in mind, the generalized hybrid mass damper (GHMD) systems are reclassified and investigated in this paper to examine diversifying needs. The variations in their modal properties and tuning effects with respect to delay time are addressed based on an explicit formula derived from a delayed exponential characteristic equation (DECE). It is found that the active control force with delay-time chosen as the natural period of the system in a HMD based on an uncompensated output feedback scheme will keep the robustness on response reduction performance. This advantage degrades for non-optimal systems with delayed control force due to the detuning effects. A detailed study is addressed to demonstrate the interaction effects of detuning and time-delay in this study. In addition to modal properties, a discrete-time state-space approach is applied to verify the control performance in time domain subjected to earthquake excitations.