Artificial Intelligence (AI) agents personalize their responses by tailoring explanations to users' backgrounds, interests, and prior interactions, referred to as contextualization. Personalization has been identified as a persuasive strategy in politics or in marketing. However, the persuasive effect of contextualization in everyday tasks, where users often lack prior knowledge, remains unclear. We conducted a $2\times2$ between-subjects experiment ($N = 380$) examining how contextualization, combined with conversational warmth, shapes reliance and persuasiveness of an AI assistant arguing against expert recommendations. Our findings reveal that contextualization reduces the persuasive power of AI, but its combination with warmth restores persuasiveness through a crossover interaction. Reliance on AI is present across conditions and is invariant to the conversational design. Trust strongly predicts both persuasion and reliance, yet neither contextualization nor warmth operates through trust. AI literacy decouples trust from behavior: more literate users report lower trust in the assistant, yet are more persuaded and more reliant on its advice. These results suggest that users are prone to deferring to AI agents over human expert judgment; however, interface-level conversational design choices have a limited role in shaping the behavior.