Temporal Action Localization (TAL) is a complex task that poses relevant challenges, particularly when attempting to generalize on new -- unseen -- domains in real-world applications. These scenarios, despite realistic, are often neglected in the literature, exposing these solutions to important performance degradation. In this work, we tackle this issue by introducing, for the first time, an approach for Unsupervised Domain Adaptation (UDA) in sparse TAL, which we refer to as Semantic Adversarial unsupervised Domain Adaptation (SADA). Our contribution is threefold: (1) we pioneer the development of a domain adaptation model that operates on realistic sparse action detection benchmarks; (2) we tackle the limitations of global-distribution alignment techniques by introducing a novel adversarial loss that is sensitive to local class distributions, ensuring finer-grained adaptation; and (3) we present a novel experimental setup, based on EpicKitchens100, that evaluates multiple types of domain shifts in a comprehensive manner. Our experimental results indicate that SADA improves the adaptation across domains when compared to fully supervised state-of-the-art and alternative UDA methods, attaining a relative performance boost of up to 14%.