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Emotion-Cause Pair Extraction in Conversations (ECPEC) aims to identify the set of causal relations between emotion utterances and their triggering causes within a dialogue. Most existing approaches formulate ECPEC as an independent pairwise classification task, overlooking the distinct semantics of emotion diffusion and cause explanation, and failing to capture globally consistent many-to-many conversational causality. To address these limitations, we revisit ECPEC from a semantic perspective and seek to disentangle emotion-oriented semantics from cause-oriented semantics, mapping them into two complementary representation spaces to better capture their distinct conversational roles. Building on this semantic decoupling, we naturally formulate ECPEC as a global alignment problem between the emotion-side and cause-side representations, and employ optimal transport to enable many-to-many and globally consistent emotion-cause matching. Based on this perspective, we propose a unified framework SCALE that instantiates the above semantic decoupling and alignment principle within a shared conversational structure. Extensive experiments on several benchmark datasets demonstrate that SCALE consistently achieves state-of-the-art performance. Our codes are released at this https URL.