We consider the problem of stabilizing multi-evaporator vapor-compression cycle (ME-VCC) systems using decentralized controllers. ME-VCC systems, sometimes termed variable-refrigerant-flow systems, are prevalent in large buildings that maintain independent cooled spaces with a single heat rejection unit. We exploit the time-scale separation characteristic of ME-VCC systems and analyze the faster mass flow dynamics and their stability characteristics independently of the slower thermal dynamics in the system. An electrical circuit analogy is used to obtain a linearized state-space representation of the mass flow dynamics for two common architectures of ME-VCC systems. Using concepts from decentralized control theory, we provide conditions under which local static feedback controllers stabilize the overall closed-loop system with robustness to uncertainties in the coupling between subsystems. Our analysis characterizes the beneficial impact that discharge pressure regulating (DPR) valves have on the decentralized controller gains.