As Generative AI (GenAI) chatbots are increasingly used for everyday health guidance, understanding how explanation-based design fosters responsible reliance is critical for user safety and wellbeing. This study investigates whether communication transparency, operationalized through brief, user-facing explanations that justify recommendations, increases users’ intention to follow (ITF) such advice. Drawing on dual-process perspectives, a parallel mediation model is proposed where transparency influences ITF through two psychological mechanisms: perceived AI agency (a socialrelational pathway) and perceived AI competence (a cognitive-evaluative pathway). A quantitative, single-factor, between-subjects online experiment (N = 151) randomly assigned participants to either high- or low-transparency GenAI health recommendations within a wellness scenario. Results show that transparency significantly increases ITF AI advice. Mediation analyses reveal that this effect occurs indirectly through enhanced perceptions of both agency and competence, with competence emerging as the stronger driver - suggesting that users prioritize demonstrated expertise over social attribution in health-related decisions. These findings advance human-AI interaction research and offer strategic guidance for health-tech developers by highlighting that transparent, evidence-based reasoning is a primary driver of user adherence in AI-mediated healthcare.