World Action Models (WAMs) advance beyond conventional visuomotor policies by jointly predicting future world states and robot actions, enabling the policy to learn physical dynamics that support effective control. However, recent tactile WAMs often rely on large-scale pretrained generative backbones to capture contact-rich physical dynamics, which limit their inference efficiency and flexible deployment. In this paper, we present \ABBR{}, an agile tactile World Action Model for contact-rich robot control. \ABBR{} encodes visual and tactile observations into a shared latent that serves as the source of a direct vision-tactile-to-action flow-matching process, which can jointly generate latent representations of action chunks and future visual/tactile latents. A key observation is that vision and tactile signals evolve at inherently different timescales: adjacent visual frames are often highly similar, whereas tactile signals can change abruptly upon contact. We therefore introduce multi-horizon multimodal prediction in \ABBR{}, which provides supervision for visual latent at a larger temporal offset while predicting the tactile latent in the next frame to capture fine-grained contact dynamics. Across nine simulated and five real-world contact-rich manipulation tasks, \ABBR{} demonstrates strong and robust performance, outperforming the strongest baseline in success rate while maintaining low inference latency. In particular, in five real-world experiments, \ABBR{} yields a relative gain of
29.4% in overall success rates while achieving inference latency of
11.9 ms. These results demonstrate that multimodal WAM can be achieved with an agile architecture suitable for precise and high-frequency robot control. More details are available on our project page: https://hanchuzhou.github.io/TARO_project_page/.