In the final "Last-Centimeter" phase of manipulation, where visual occlusion or calibration errors render vision unreliable, robots often suffer high failure rates due to local pose uncertainty and simulation dynamics deviations. To address these issues, this paper proposes the PECHC (Physics-Evolving Cascade Constraint and Human-Correction) algorithm. To rigorously isolate the contribution of tactile feedback in multi-finger coordination, we adopt a decoupled control strategy that focuses on grasp stabilization within the hand's workspace, acting as a fail-safe reflex. The core of our approach is Hybrid Correction Imitation Learning (HCIL), which establishes a "failure-triggered" human-machine mechanism to efficiently resolve the "model gap" via sparse expert corrections. To ensure sample efficiency and baseline performance, we introduce two supporting modules: Cascaded Constraint Scheduling (CCS) addresses the "geometric gap" by enforcing physically plausible behavioral constraints (geometric approach, force closure, and dynamic stability), while Temporal Heterogeneous Distillation (THED) resolves the "physical gap" by enabling implicit system identification from tactile history. Experiments demonstrate that PECHC achieves a 97.3% real-robot success rate on 150 objects from the Visual Dexterity Dataset under fully autonomous testing, where one object is used for one-time HCIL calibration and the remaining 149 objects are evaluated without further intervention. Compared to a standard Sim-to-Real reinforcement learning baseline (Vanilla PPO with Domain Randomization), PECHC delivers a significant performance improvement (+42.8%) and exhibits human-like force modulation capabilities for fragile objects.