Notification issues with iPhone when paired with Apple Watch

For Pushover notifications to appear on your Apple Watch, it needs to be secure on your wrist, unlocked, and your iPhone needs to have its screen off.  When in this mode, if you have Notification Mirroring enabled for the Pushover app (configurable inside the Watch app on the iPhone), the notification will appear on your watch.  Note that custom notification sounds are not supported on Apple Watch.

To continue hearing notification sounds on your iPhone even when your Apple Watch is on your wrist, you will need to disable Notification Mirroring for the Pushover application which will stop showing any Pushover notifications on the Watch.  You can do this by opening the Watch app on your iPhone, then select Notifications, then uncheck Pushover.