Directed acyclic graph (DAG)-based Byzantine Fault-Tolerant (BFT) protocols achieve high throughput by decoupling dissemination from agreement and allowing many vertices to be committed concurrently. This same concurrency, however, weakens ordering evidence at the execution boundary: once units are committed in a shared DAG frontier, their final linearization is driven by traversal or deterministic tie-breaking rather than verifiable structural precedence. Prior fair-ordering designs address ambiguity by collecting or reconstructing transaction-level ordering evidence within the consensus workflow. While effective, this couples ordering with agreement and places ordering logic on the critical path. This paper presents Multi-Round Visibility (MRV), a post-consensus structural ordering layer for DAG-based BFT that reinterprets the committed DAG as an ordering evidence substrate. Committed vertices inherently carry authenticated creator, round, and ancestry metadata, enabling replicas to derive multi-round structural visibility without extra consensus-path messages. MRV accumulates this visibility within a bounded evidence horizon, compares concurrently committed atomic units of fairness (AUFs) after they coexist in the DAG, and derives precedence constraints from Byzantine-robust visibility advantages. When the DAG lacks such constraints, MRV exposes and resolves the remaining ambiguity through deterministic graph completion rather than hiding it inside traversal rules. We implement MRV on a Narwhal/Tusk-based prototype. Evaluation across 5-50 replicas under various fault settings shows MRV preserves the high-throughput regime of the DAG-BFT stack, proving it provides post-consensus structural ordering without burdening the consensus-critical path.