Cue syncs through your iCloud account. Make sure every device is signed in to the same Apple ID and that iCloud is enabled for Cue in Settings. Sync usually completes within a few seconds of a change.
Check that notifications are allowed for Cue in Settings › Notifications, and that a Focus mode or Cue's own quiet hours aren't suppressing them.
Open the Watch app on your iPhone, find Cue under Available Apps, and tap Install.
For anything else, email cue@tutu.casa and include your device model and iOS/watchOS/macOS version if the question is about a problem.