In order to better understand and predict the complex interface instability phenomena induced by non-uniform shock waves in practical engineering and scientific applications, a detailed investigation has been conducted on the interaction between a Mach reflection wave configuration and a planar gas interface. Particular attention is paid to the role of the Mach stem scale in governing the evolution of interface instability and the associated mechanisms of perturbation growth. Numerical simulations show that when the Mach reflection wave configuration interacts with the interface, the complex wave structures impart initial velocity perturbations onto the interface, thereby triggering instability. This process is further influenced by the non-uniform post-shock flow field, under which the initially perturbed interface gradually evolves into a concave cavity and subsequently into jet-like bubble structures. These patterns are notably different from the spike and bubble morphologies observed in classical Richtmyer-Meshkov instability. A systematic quantitative analysis of the perturbation amplitude reveals that the instability growth can be divided into two different stages: an initial linear growth stage and a nonlinear development stage. The transition between these stages is governed by interface deformation mechanisms, particularly the bending of the slip line intersecting the interface and the subsequent formation of the curl-up jet. When the shock strength and incidence angle of the Mach reflection configuration are kept constant, the Mach stem scale emerges as the decisive parameter controlling the characteristic time of slip line curling and jet development. The results show that during the linear stage, perturbation growth is primarily determined by shock strength and incidence angle, and is insensitive to the Mach stem scale. In contrast, during the nonlinear stage, the perturbation growth rate increases with the augmentation of Mach stem scales, highlighting the scale-dependent nature of the nonlinear stage. Furthermore, theoretical models are critically examined against numerical simulation results. While existing models can reasonably capture the initial velocity perturbations imprinted on the interface by the Mach reflection configuration, they are unable to combine the effects of Mach stem scale and the sustained driving influence of post-shock flow non-uniformities. This limitation underscores the need for improved theoretical descriptions. Overall, these findings provide new insights into the intrinsic coupling among shock strength, incidence angle, and Mach stem scale in determining the evolution of shock-induced interface instability. These insights not only deepen the fundamental understanding of the non-stand RM instability but also provide valuable references for the development of predictive theoretical models and the engineering applications such as inertial confinement fusion and high-speed propulsion systems.