Just-in-Time Adaptive Interventions (JITAIs) are envisioned to harness rich data on users' contexts. However, many JITAIs fall short in leveraging the value of the data while sculpting the interventions. Investigating the literature reveals a lack of user-centered design (UCD) methods in designing JITAIs. Our case study of applying a UCD process revealed that even without deploying a JITAI, UCD could uncover user interactions that inform critical design decisions of a JITAI's components. We reflect on our experiences engaging in a user-centered JITAI design process and urge the broader human-computer interaction (HCI) community to devise concrete design guidelines for JITAIs. We take the first step toward that goal by proposing a checklist of key design considerations for future JITAIs. Together, this case study contributes insights on applying UCD to the design of all components of a JITAI, which can help capture users' needs and provide actionable interventions.