In this article, we propose a control architecture for the safe, coordinated operation of a multi-agent system with aerial (UAVs) and ground (UGVs) robots in a confined task space. We consider the case where the aerial and ground operations are coupled, enabled by the capability of the aerial robots to land on moving ground robots. The proposed method uses time-varying Control Barrier Functions (CBFs) to impose safety constraints associated with (i) collision avoidance between agents, (ii) landing of UAVs on mobile UGVs, and (iii) task space restriction. Further, this article addresses the challenge induced by the rapid increase in the number of CBF constraints with the increasing number of agents through a hybrid centralized-distributed coordination approach that determines the set of CBF constraints that is relevant for every aerial and ground agent at any given time. A centralized node (Watcher), hosted by an edge computing cluster, activates the relevant constraints, thus reducing the network complexity and the need for high onboard processing on the robots. The CBF constraints are enforced in a distributed manner by individual robots that run a nominal controller and safety filter locally to overcome latency and other network nonidealities.