Large Reasoning Models (LRMs) often reach a correct solution before their long Chain-of-Thought trace ends, yet continue with redundant verification, repeated attempts, or unnecessary exploration that wastes computation and can even overturn the correct answer. We frame this behavior as a latent productive-to-redundant transition and show that it is directly reflected in hidden states: around first-correct-solution (FCS) boundaries, late-layer representations separate efficient from overthinking tokens, while boundary-permutation and position-control baselines collapse. Based on this signal, we propose ROM, a model-agnostic streaming intervention framework that monitors frozen LRMs with a lightweight hidden-state detector and intervenes at well-formed reasoning boundaries. Counterfactual Self-Correction (CSC) augments supervision with balanced wrong to correct trajectories, preserving useful pre-FCS correction while labeling only post-FCS continuation as redundant. Across MATH500, GSM8K, AIME25, and MMLU-Pro, ROM improves the overall tradeoff on both Qwen3-8B and DeepSeek-R1-Distill-Qwen-32B (DS-32B): on Qwen3-8B, it raises accuracy from 74.47% to 74.78% and reduces response length from 4262 to 3107 tokens; on DS-32B, it raises accuracy from 68.60% to 68.72% and reduces response length from 3062 to 2319 tokens. The same FCS-derived supervision transfers across scale and training origin, suggesting a shared long-CoT boundary rather than a backbone-specific artifact. ROM is compatible with L1, removing another 20.9-21.6% tokens at zero accuracy loss. ROM also generalizes to open-ended MMLU-Pro (+1.56 pp, 35.4% shorter) and reduces wall-clock latency by 46.5%. Code is available at https://github.com/SaFo-Lab/ROM.