I’m not sure, if i understood your problem correctly, but your have 2 basic ways to trigger application behaviour.
1) Via the actions-File, to tell certain nodes to start certain actions at a certain time.
2) Via the reception of messages to your application. You can implement a MessageHandler to trigger application-internal behaviour after receiving a message of a specific type or content. You would have to implement either DHT or KBR-based message handlers (wheather you use KBR or DHT message forwarding in the overlay).