We formulate and analyze an operational test of a tacit assumption frequently made in quantum device modeling: that the reduced density matrix ρS of a subsystem S is a sufficient state variable for predicting its future reduced evolution under fixed declared controls. We formalize this assumption as Local Evolution Completeness (LEC): if two global preparations share the same reduced state ρS(0), then they must yield identical ρS(t) under identical device dynamics. We first establish a strict-locality null result: when the applied Hamiltonian factorizes as HS ⊗ IE, LEC holds exactly, independent of correlations with ancillary degrees of freedom. We then prove, via an explicit process-tensor counterexample, that LEC can fail even when all intermediate maps are completely positive and trace-preserving and the global dynamics is strictly unitary. In such cases, no reduced map Φ exists with ρS(t) = Φ(ρS(0)) for all embeddings realizing the same ρS(0). To operationalize this distinction, we construct a fully solvable qubit–ancilla model and derive closed-form reduced trajectories, along with a statistical inference framework for detecting preparation-dependent deviations under fixed controls. We provide microscopic realizations of the embedding variable responsible for LEC failure, including correlation-invariant and control-reference mechanisms. The proposed protocol isolates a distinct experimental axis from traditional nonlinear quantum mechanics tests: it probes the predictive sufficiency of reduced states rather than convex linearity of state evolution. A violation of LEC would not imply a modification of global unitary dynamics, but rather demonstrate that single-time reduced density matrices are not sufficient statistics for multi-time prediction in the tested setting. This clarifies the structural role of reduced states within the operational foundations of quantum theory.