We construct a new numerical modeling for two-phase immiscible flow in a strongly heterogeneous deformable carbonate underneath a rock salt composed by halite and anhydrite displaying creep behavior with the viscous strain ruled by a nonlinear constitutive law of power-law type. Within the framework of the so-called iteratively coupled methods and fixed-stress split algorithm we develop mixed finite element methods for the flow and geomechanics subsystems which furnish locally conservative Darcy velocity and transient porosity input fields for the transport problem for the water saturation. Such transport equation is decomposed within an operator splitting technique based on a predictor-corrector scheme with the predictor step discretized by a higher-order non-oscillatory finite volume central scheme. Numerical simulations of a water-flooding problem in secondary oil recovery are presented for different realizations of the input random fields (permeability, Young modulus and initial porosity). Comparisons between the accuracies of the proposed approach and the traditional one-way coupled hydro-geomechanical formulation are presented. In addition, simulations including the viscoelastic behavior of the overburden rock salt are performed showing the effects of salt stiffness and irreversible deformation upon finger grow and breakthrough curves. A notable feature of the formulation proposed herein is the accurate prediction of the influence of geomechanical effects upon the unstable movement of the water front, whose evolution is dictated by carbonate heterogeneity, unfavorable viscosity ratio and geomechanical effects without deteriorating the local conservative character of the numerical schemes. 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