Generative artificial intelligence (AI) systems such as ChatGPT and DeepSeek require users to disclose nuanced prompts that may reveal highly sensitive personal information. Existing studies on privacy risks in generative AI are fragmented and rarely grounded in established privacy theories or comparative frameworks. To advance knowledge on generative AI privacy, a multi-stage model of privacy decision-making is proposed that integrates machine heuristics, privacy concerns, privacy cynicism and self-disclosure. Drawing on two online surveys in China and the US (N = 1632), we examine how machine heuristic perceptions relate to privacy concerns, how concerns translate into privacy cynicism, and how cynicism is associated with self-disclosure. Chinese respondents reported higher self-disclosure, whereas US participants expressed greater privacy concerns, mistrust and uncertainty, but also higher self-efficacy and use frequency. The findings suggest that perceptions of AI as fair, accurate, and having expertise are associated with lower privacy concerns, that concerns are positively linked to cynicism dimensions, and that cynicism exhibits divergent associations with self-disclosure. These results are discussed and contextualized in relation to privacy scholarship and policy and design recommendation.