The field of robotic manipulation has advanced significantly in recent years. At the sensing level, several novel tactile sensors have been developed, capable of providing accurate contact information. On a methodological level, learning from demonstrations has proven an efficient paradigm to obtain performant robotic manipulation policies. The combination of both holds the promise to extract crucial contact-related information from the demonstration data and actively exploit it during policy rollouts. However, this integration has so far been underexplored, most notably in dynamic, contact-rich manipulation tasks where precision and reactivity are essential. This work therefore proposes a multimodal, visuotactile imitation learning framework that integrates a modular transformer architecture with a flow-based generative model, enabling efficient learning of fast and dexterous manipulation policies. We evaluate our framework on the dynamic, contact-rich task of robotic match lighting - a task in which tactile feedback influences human manipulation performance. The experimental results highlight the effectiveness of our approach and show that adding tactile information improves policy performance, thereby underlining their combined potential for learning dynamic manipulation from few demonstrations. Project website: https://sites.google.com/view/tactile-il .