Consistent mass-momentum (CMOM) transport methods have attracted increasing interest for multiphase flow simulations due to their robustness and adherence to key physical conservation laws, such as momentum and energy preservation [1]. However, CMOM replaces the advection of a continuous velocity field with that of a discontinuous momentum field, which can induce severe momentum shocks when coupled with sharp-interface methods. Such behavior is not adequately handled by conventional shock- capturing schemes and has motivated the recent development of monotonicity-preserving multiphase flux limiters [2, 3, 4]. In this work, we introduce an additional physical requisite, an entropy condition that justifies these monotonicity requirements for incompressible multiphase formulations, thereby providing a physically-grounded criterion for admissible momentum fluxes. We further identify a connection between the entropy condition and changes in enstrophy, enabling a quantitative assessment of numerical dissipation and robustness. By combining the current framework and the method of [2], we propose a synchronized donor-region method for momentum fluxes that enforces monotonicity while preserving momentum conservation. The proposed algorithm effectively suppresses spurious velocity oscillations while maintaining momentum conservation. Validation is demonstrated using canonical traveling droplet simulations, down to density ratios of 10^−9, and perturbation growth of Kelvin-Helmholtz instability. Applicability to more complex flows is further illustrated through standing breaking wave simulations.