The concept of On-Demand Mobility (ODM) in aviation has gained popularity in recent years, with several manufacturers proposing vehicles for high-speed intra-city air taxis. However, less attention has been placed on how these fleets would be operationally controlled and managed. Through the development of concepts of operations for remote management of vehicles with differing levels of autonomy, this paper presents preliminary requirements for ODM air operations control centers. The centers would interface with air traffic control and be responsible for ensuring safe, efficient, and effective operations of fleets within subareas of the National Airspace System. Our effort identified key functional requirements related to vehicle safety, customer experience, and airspace integration for these futuristic concepts. Further, this work introduces a novel Remote Operations Center (ROC) concept with highly integrated human-machine systems for efficient operations with limited staffing. The ROC would support the transition from providing dispatcher-like support to supervisory control of autonomous ODM systems, including managing emergencies, which will be crucial for operational success as vehicle autonomy evolves.