Identical linguistic expressions can convey different sentiments across cultural contexts. Yet, current multilingual models often reduce language to mere symbolic representation, neglecting the cultural pragmatics that fundamentally shape affective semantics in Sentiment Analysis (SA). Due to this oversight, the systematic performance degradation of Small Multilingual Language Models (SMLMs) on culturally distant targets is frequently attributed to resource constraints. This perspective obscures the pivotal role of cultural pragmatics, an intrinsic determinant of affective semantics, and thereby conceals cultural misalignment as the principal structural bottleneck. In this paper, we conduct a comprehensive empirical study to quantify the influence of culture on cross-lingual sentiment transfer across 7 common SMLMs and 5 linguistically diverse languages. By fitting a Linear Mixed-Effects Model (LMEM) on over 300 experimental runs, we disentangle cultural factors from confounding variables. Our results reveal that Cultural Distance is a significant, independent, negative predictor of transfer performance. Furthermore, representation probing and qualitative error analysis uncover a pragmatic alignment paradox: while SMLMs encode cultural distinctions, they fail to map these representations to downstream sentiment labels in high-context cultures. Ultimately, our work enhances the interpretability of cross-lingual transfer failures by statistically isolating cultural misalignment as a structural barrier, distinct from the resource constraints typically blamed for poor performance.