Besides numerous experimental reports revealing the characteristic dependence of depression on liquid surfaces induced by impinging plasma beams, and despite its scientific and practical importance, the physical mechanism responsible for this dependency has been missed. In this study, based on the border electrons' role, the water/plasma interfacial dynamics relevant to electrohydrodynamic instability (EHD) have been theoretically modeled, focusing on the characteristic dependence of the EHD growth rate driven by charge mobility mechanisms. The predictions of the growth rates dependent on water conductivity from theory agree well with our observations of faster plasma-filled underwater bubble explosions under lower conductivity conditions, indicating that the model contains the essence of the underlying physics of liquid surface deformation in the presence of plasma.