The standard way to do timing in a system like this is for each subsystem to run its own binary clock, with the main system sending period time-of-day messages

The standard way to do timing in a system like this is for each subsystem to run its own binary clock, with the main system sending period time-of-day messages to keep everything externally synchronized. In that sense, all the systems do have one clock. Many do not need to worry about wall clock time or synchronization, though.