The file/database-backed persistent timer service implementation consolidates timeout events that would trigger in the past. For example, take a single server with a timer that execute every 10 seconds. If the server is shutdown for 1 minute, upon restart, the timer service triggers a single timeout in lieu of the 6 missed timeout events.
Currently, the distributed timer service will emit all missed events in sequence until it arrives at a timeout that will schedule in the future.
The Jakarta Enterprise Bean specification only says this, on the subject:

In the event of a container crash or container shutdown, the timeout callback method for a persistent timer that has not been cancelled will be invoked on a new JVM when the container is restarted or on another JVM instance across which the container is distributed.

The old persistent timer service interprets this to mean that all missed timeouts for a given timer will consolidate to a single event. For continuity, the Infinispan-based distributed timer service should behave in the same way.