Autonomous software agents hold promise to increase developer productivity but make mistakes and exhibit novel failure modes, making human oversight central to successful human-agent collaboration. Existing research on agent oversight is largely conceptual; normative frameworks exist, but how users actually oversee agents is less known. In this paper, we bridge this gap by providing early empirical anchors for the theoretical discourse on agent oversight. Drawing on interviews with 17 experienced developers, we conduct an exploratory inquiry examining what forms of emergent oversight work developers perform, when, and how. We also document the oversight challenges developers face and the strategies they have started using to address them. We found at least four forms of emergent oversight work: a priori control, co-planning, real-time monitoring, and post hoc review. We show that oversight work is not only reactive and retrospective, as portrayed in existing research, but also preventative and proactive. We describe situated oversight challenges (e.g., difficulty reviewing agent-generated code) and outline heuristics developers adopt to address such challenges (e.g., using test results as guarantees for code correctness). We conclude with high-level takeaways, future research directions, implications for the human-centered design of software agents and for software engineering practice, and limitations of our research.