I experienced the same thing, and it frustrated me so much that I tried to find the solution. Here it is:
1. On your smartwatch, open settings then go to notifications.
2. From there, scroll to the bottom to see Wireless emergency alerts.
3. From there, scroll down again to Alert preferences, then Alert reminder. Choose NEVER or whichever you prefer.
That's it. It worked for me; I hope it does the same to you.