Safe L2/L3 driving automation requires anticipating human-in-the-loop reactions during shared-control transitions. While most driving world models forecast the external environment, in-cabin intelligence remains strictly recognition-oriented and lacks multi-step rollout capabilities for driver dynamics. We introduce Driver-WM, a driver-centric latent world model that rolls out in-cabin dynamics causally conditioned on out-cabin traffic context. This formulation unifies physical kinematics forecasting with auxiliary behavioral and emotional semantic recognition. Operating in a compact latent space constructed from frozen vision-language features, Driver-WM adopts a dual-stream architecture to separately encode external traffic and internal driver states. These streams are directionally coupled via a gated causal injection mechanism, which uses a learned vector gate to modulate external contextual perturbations while strictly enforcing temporal causality. Evaluations on a multi-task assistive driving benchmark demonstrate that Driver-WM yields robust long-horizon geometric forecasting for reactive high-motion maneuvers and improves semantic alignment for both driver and traffic states. Finally, the explicit external-to-internal conditioning allows for controlled test-time interventions to systematically analyze mechanism responses.