This is what I got since having asked the question:
The clustered service is the jboss.ejb:service=EJBTimerService, which relies on the Quartz scheduler; so basically you have to check for the Timer Service, the one that is clustered.
The Quartz scheduler doesn't need to be configured at all, if not for other specific use cases that I haven't met yet.
For solving the problem I explained, we simply configured the scheduled bean to depend to the HASingletonDeployer service, type Barrier, so that our bean is deployed as singleton on just one node at a time.
I have the same issue and the same concerns :
17:33:40,716 INFO [QuartzScheduler] Scheduler DefaultQuartzScheduler_$_NON_CLUSTERED started.
Did you fix that?