Hello Matthias,
I may be wrong here, but a Client Action, in mobile, as well as the Server/Screen Action in a Web application, only exists while the application is running. So, I can't see how would be possible to trigger a Client Action with the application closed.
But... According to the link bellow, it seems it is possible to launch an app automatically on receiving a notification:
https://stackoverflow.com/questions/30089963/how-to-automatically-open-the-app-without-user-action-on-receiving-a-push-on-and
Maybe you can adapt it to your needs.
Cheers,
Eduardo