In January 2025, the U.S. government enacted a nationwide ban on TikTok, prompting a wave of American users -- self-identified as ``TikTok Refugees'' -- to migrate to alternative platforms, particularly the Chinese social media app RedNote (Xiaohongshu). This paper examines how these digital migrants navigate cross-cultural platform environments and develop adaptive communicative strategies under algorithmic governance. Drawing on a multi-method framework, the study analyzes temporal posting patterns, influence dynamics, thematic preferences, and sentiment-weighted topic expressions across three distinct migration phases: Pre-Ban, Refugee Surge, and Stabilization. An entropy-weighted influence score was used to classify users into high- and low-influence groups, enabling comparative analysis of content strategies. Findings reveal that while dominant topics remained relatively stable over time (e.g., self-expression, lifestyle, and creativity), high-influence users were more likely to engage in culturally resonant or commercially strategic content. Additionally, political discourse was not avoided, but selectively activated as a point of transnational engagement. Emotionally, high-influence users tended to express more positive affect in culturally connective topics, while low-influence users showed stronger emotional intensity in personal narratives. These findings suggest that cross-cultural platform migration is shaped not only by structural affordances but also by users' differential capacities to adapt, perform, and maintain visibility. The study contributes to literature on platform society, affective publics, and user agency in transnational digital environments.