The versatile regulatory capacity of pumped storage power station (PSPS) stems from the reversible pumped turbine unit switching between multiple operating conditions. Nevertheless, the unit and plant structure experience heightened vibrations owing to the intricate interplay of hydraulic, electrical, and mechanical excitations during transition processes, and the vibration responses fluctuate as operating conditions shift, posing a significant challenge to the safety and high quality operation of power station. To tackle the practical engineering issue, this paper delves into the sudden load-up scenario in power generation situation of pumped turbine, leveraging a finite element model encompassing the coupled hydraulic-mechanical-electrical-structural system (HMES) of PSPS and a mathematical model of unit shaft system, the impacts of dynamic loads induced by various vibration source on the unit and plant structure during transient condition, are meticulously analyzed and discussed through numerical simulations. Additionally, the magnetorheological damper (MRD), is incorporated into the PSPS to explore the effectiveness of MRD in controlling transient vibration in the interconnected unit-plant structure. The results indicate that the system parameters and associated load excitations undergo rapid fluctuations during the load-up process, bringing about noticeable oscillations in vibration amplitudes of rotor and turbine. The floors and fan hood of plant are the most vulnerable areas in terms of structural strength, with associated displacement amplitudes being most noticeable. The incorporation of MRD proves to be highly effective in mitigating the unsteady vibrations in both the unit and the plant structure during load-up course, as well as optimizing the motion patterns of rotor and turbine, promoting a notable reduction in frequency amplitudes of spectrum. Moreover, the maximal transient displacement amplitude of unit is significantly diminished, with the rotor experiencing a decrease of approximately 79%, while the amplitude of turbine declines by 16%. The displacement fluctuation ranges of the plant structure are observably diminished, and the complex frequency components of vibration signal are efficiently controlled. The transient vibration characteristics of the coupled unit-plant structure and the damping behavior of MRD during the transition process are unveiled by the research findings in this paper, which can offer valuable insights for the stability assessment and the research on vibration management of HMES for PSPS under the unsteady operation conditions.