AI coding assistants are commonly used for daily software development tasks. While prior research has examined their impact on productivity and code quality, less is understood about how these tools support diverse ways of thinking. Evidence from non-AI software engineering tools suggests that mismatches between tool design and users' cognitive styles can introduce inclusivity barriers, but it remains unclear whether similar issues arise in AI coding assistants. We investigate how developers with different cognitive styles experience and interact with these tools and whether they exhibit cognitive inclusivity challenges. We conducted a controlled laboratory study with 20 student participants using GitHub Copilot to complete code generation, debugging, and refactoring tasks. Using think-aloud protocols, semi-structured interviews, and inductive thematic analysis, we identify patterns in user interaction. We then apply the GenderMag framework to examine how these patterns differ across cognitive styles. We identify five inclusivity issues concerning how Copilot explains suggestions, supports validation, facilitates learning, exposes its features, and influences the problem-solving process. Our findings suggest that common interaction paradigms in AI coding assistants can privilege certain cognitive styles while introducing additional cognitive effort for others. We derive design implications for more inclusive AI coding assistants.

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