Physicists, physics students, and community members come together and engage with physics content through various forms of informal education programming. Our prior work has shown that the landscape of informal physics programs in the United States has a variety of formats, audience demographics, and content. Informal physics programs have many benefits for both facilitators and community members; however, we do not fully understand how the variety of program structures, designs, and organizations affect participants' experiences. In this study, we apply an organizational theory framework to study the connectedness of six functional aspects of informal physics programs: "Assessment," "Audience," "Institution," "Personnel," "Program," and "Resources." We interview lead facilitators about the design and structure of their programs. Here we present an in-depth qualitative analysis of three cases. We find that the personnel, consisting of the faculty, staff, and physics students facilitating the educational activities, have a prominent role in these programs. Our findings show how personnel members influence the physics content, activities, and interactions with the audience. We discuss how understanding these aspects can help support improving the functionality of informal physics programs in equitable and inclusive ways.