Aligning egocentric video with wearable sensors have shown promise for human action recognition, but face practical limitations in user discomfort, privacy concerns, and scalability. We explore exocentric video with ambient sensors as a non-intrusive, scalable alternative. While prior egocentric-wearable works predominantly adopt Global Alignment by encoding entire sequences into unified representations, this approach fails in exocentric-ambient settings due to two problems: (P1) inability to capture local details such as subtle motions, and (P2) over-reliance on modality-invariant temporal patterns, causing misalignment between actions sharing similar temporal patterns with different spatio-semantic contexts. To resolve these problems, we propose DETACH, a decomposed spatio-temporal framework. This explicit decomposition preserves local details, while our novel sensor-spatial features discovered via online clustering provide semantic grounding for context-aware alignment. To align the decomposed features, our two-stage approach establishes spatial correspondence through mutual supervision, then performs temporal alignment via a spatial-temporal weighted contrastive loss that adaptively handles easy negatives, hard negatives, and false negatives. Comprehensive experiments with downstream tasks on Opportunity++ and HWU-USP datasets demonstrate substantial improvements over adapted egocentric-wearable baselines.