Dexterous manipulation is fundamentally a problem of interaction dynamics: the hand must track precise finger trajectories, regulate the contact force exchanged with grasped objects, respect actuation and safety limits, and remain predictable when contact persists -- objectives in tension for any fixed-gain controller. A sustained contact torque $τ_{\text{ext}}$ through a joint stiffness $K_d$ produces the structural bias $e_\infty=τ_{\text{ext}}/K_d$, so stiffening for accuracy sacrifices contact safety while softening yields by design. We make these interaction dynamics explicit and actuator-agnostic through a constant-$A_d$ double-integrator backbone, instantiating the offset-free architecture established for physical human-robot interaction (pHRI) and preserving its modeling assumptions on the reduced residual dynamics. An algebraic feedforward reduces the tendon transmission -- hydraulic, cable, pneumatic, twisted-string, or series-elastic -- to a constant-coefficient double integrator, so the QP cost inverse is precomputed offline and a 10-step receding-horizon QP runs at 500\,Hz under contact-force (ISO/TS 15066), actuation, and jerk constraints. An encoder-only augmented-Kalman disturbance state drives steady-state error to zero under constant contact loads in the nominal detectable case. In simulation, a hydraulically actuated finger -- the worked example, adding pressure and cavitation constraints -- attains 0.6\,mrad RMS, 0.1\,mrad steady-state, and 7.3\,mrad peak deflection under 1.5\,Nm contact: 153$\times$, 1500$\times$, and 21$\times$ better than classical impedance. The realized first-move stiffness (18$\to$323\,Nm/rad with update rate) is independently verified, and the architecture scales to a 16-DOF LEAP Hand MuJoCo model, recovering from 2.5\,N grasp disturbances within 0.7\,s.

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