Generative AI is reshaping software work, yet we lack clear guidance on where developers most need support and how to design it responsibly. We report a large-scale, mixed-methods study of N=860developers examining where, why, and how they seek or limit AI across SE tasks. Using cognitive appraisal theory, we provide the first empirically validated mapping of developers’ task appraisals to AI adoption patterns and Responsible AI (RAI) priorities. Appraisals predict AI openness and use, revealing distinct patterns: strong current use and demand for improvement in core work (e.g., coding, testing); high demand to reduce toil (e.g., documentation, operations); and clear limits for identity- and relationship-centric work (e.g., mentoring). RAI priorities vary by context: reliability and security for systems-facing tasks; transparency, alignment, and steerability to maintain control; and fairness and inclusiveness for human-facing work. Our results offer concrete, contextual guidance for delivering AI where it matters to developers and their work.