Autonomous AI agents are transforming software development and redefining how developers collaborate with AI. Prior research shows that the adoption and use of AI-powered tools differ between core and peripheral developers. However, it remains unclear how this dynamic unfolds in the emerging era of autonomous coding agents. In this paper, we present the first empirical study of 9,427 agentic PRs, examining how core and peripheral developers use, review, modify, and verify agent-generated contributions prior to acceptance. Through a mix of qualitative and quantitative analysis, we make four key contributions. First, a subset of peripheral developers use agents more often, delegating tasks evenly across bug fixing, feature addition, documentation, and testing. In contrast, core developers focus more on documentation and testing, yet their agentic PRs are frequently merged into the main/master branch. Second, core developers engage slightly more in review discussions than peripheral developers, and both groups focus on evolvability issues. Third, agentic PRs are less likely to be modified, but when they are, both groups commonly perform refactoring. Finally, peripheral developers are more likely to merge without running CI checks, whereas core developers more consistently require passing verification before acceptance. Our analysis offers a comprehensive view of how developer experience shapes integration offer insights for both peripheral and core developers on how to effectively collaborate with coding agents.