The Signal server would send a backend notification to the client app via the Apple Push Notification Service. The app is then able to wake up, at which point it fetches new messages (securely) from the Signal servers. The app then generates a local notification with a preview of the received message. iOS is then logging those messages.
The Signal server would send a backend notification to the client app via the Apple Push Notification Service. The app is then able to wake up, at which point it fetches new messages (securely) from the Signal servers. The app then generates a local notification with a preview of the received message. iOS is then logging those messages.