Hi
After your Apple Watch has been used to contact the emergency services via the SOS feature, it is normal - unless you choose to cancel - for your watch to send text messages to your SOS contacts for a period of time afterwards, advising them of your current location.
If your location changes, your contacts will be sent an update and you will receive a notification about 10 minutes later.
To stop the updates from being sent, select Stop Sharing in the notification that you receive. If you keep sharing, you will receive a reminder to stop every 4 hours for 24 hours.
More information:
About SOS on Apple Watch - Apple Support
https://help.apple.com/watch/#/apd4ea933124