How notifications behave depends on the status of your devices. In order to bring notifications to your attention as soon as possible:
- If your iPhone is unlocked, you will receive notifications on your iPhone instead of on your watch.
- If your iPhone is locked or asleep and your watch is unlocked and on your wrist, you will receive notifications on your watch.
- If your watch is locked or has Do Not Disturb enabled, notifications will go to your iPhone.
About notifications on your Apple Watch - Apple Support
You will find that if you turn off Wrist Detection (on your iPhone, in the Watch app, go to: My Watch> General> Wrist Detection) it will cause all notification alerts to be delivered to both devices. However, you will not then be able to benefit from features including Apple Pay and a single unlock after placing the watch on your wrist.
Apple Watch does not presently support alerts with custom tones / sounds for messages, emails or phone calls from specified contacts.
If you would like Apple to consider adding either or both of these as new features, you can suggest them here:www.apple.com/feedback/watc...