This study investigates cross-cultural differences in the perception of AI-driven chatbots between Germany and South Korea, focusing on topic dependency and explainability. Using a custom AI chat interface, ExplainitAI, we systematically examined these factors with quota-based samples from both countries (N = 297). Our findings revealed significant cultural distinctions: Korean participants exhibited higher trust, more positive user experience ratings, and more favorable perception of AI compared to German participants. Additionally, topic dependency was a key factor, with participants reporting lower trust in AI when addressing societally debated topics (e.g., migration) versus health or entertainment topics. These perceptions were further influenced by interactions among cultural context, content domains, and explainability conditions. The result highlights the importance of integrating cultural and contextual nuances into the design of AI systems, offering actionable insights for the development of culturally adaptive and explainable AI tailored to diverse user needs and expectations across domains.