Imbalance vibration is the main factor affecting the stability of rotating machineries equipped with active magnetic bearings (AMB). Accordingly, for safe and reliable operation, ISO 14839 standard sets out guidelines for measuring and evaluating the vibration and stability. However, technical approaches to realize fulfillment of the evaluation criteria have never been studied in theory. This paper presents insights of these criteria and proposes effective methods to simultaneously implement these evaluation criteria. Based on imbalance vibration model of AMB-rotor system, the theoretical connections between these evaluation indices are revealed. In order to obtain accurate vibration model of single-input single-output (SISO) AMB-rotor system, modal analysis is carried out and equivalent mass of SISO system is figured out. Afterwards, with the analysis of sensitivity function in theory, new indices of the evaluation criteria are proposed, which helps establish requirements of controller design and rotor balance quality. Finally, through experimental verification on a test rig, the limitations on the evaluation criteria can be negligible, and the proposed methods to simultaneously implement the evaluation criteria are validated.