Tendon-driven continuum robots offer intrinsically safe and contact-rich interactions owing to their kinematic redundancy and structural compliance. However, their perception often depends on external sensors, which increase hardware complexity and limit scalability. This work introduces a unified multi-dynamics modeling framework for tendon-driven continuum robotic systems, exemplified by a spiral-inspired robot named Spirob. The framework integrates motor electrical dynamics, motor-winch dynamics, and continuum robot dynamics into a coherent system model. Within this framework, motor signals such as current and angular displacement are modeled to expose the electromechanical signatures of external interactions, enabling perception grounded in intrinsic dynamics. The model captures and validates key physical behaviors of the real system, including actuation hysteresis and self-contact at motion limits. Building on this foundation, the framework is applied to environmental interaction: first for passive contact detection, verified experimentally against simulation data; then for active contact sensing, where control and perception strategies from simulation are successfully applied to the real robot; and finally for object size estimation, where a policy learned in simulation is directly deployed on hardware. The results demonstrate that the proposed framework provides a physically grounded way to interpret interaction signatures from intrinsic motor signals in tendon-driven continuum robots.