This issue is happening because of the difference in the way garbage collection is handled in the Editor Playmode compared to Runtime.
In Runtime (Standalone) the garbage collector does not run if it is not explicitly called whereas in Playmode it runs automatically.

Because PlayableOutputs hold only a weak reference to the receiver objects they will be garbage collected in playmode unless they are referenced somewhere else. With receivers getting destroyed of course nothing happens.

An easy way to fix this is to manage their lifetime in the PlayTimelineWithSetup monobehaviour or notification receiver class, for example they can be held in a static list in the notification receiver class in this way.

private static List<SomeNotificationReceiver> managedReceivers = new List<SomeNotificationReceiver>();
public static void Setup(PlayableGraph graph)
{
managedReceivers.Clear();
for (int i = 0; i < graph.GetOutputCount(); i++)
{
var notif = new SomeNotificationReceiver();
graph.GetOutput(i).AddNotificationReceiver(notif);
managedReceivers.Add(notif);
}
}

That way they will be referenced until a new setup is called and won't be destroyed during the first frame.