How do I disable the "Airtag Found..." notification on my families devices?

Per chance, did they have something of yours that has this AirTag attached to ... like your car keys, & then borrowed your car? If so, then the AirTag is working as designed.

The map, with the dashed lines, would indicate to the observer that an AirTag (which is not associated with their Apple ID) was traveling with them and where this occurred.

Again, this is per design to protect people from being tracked.

Note, at the present time, Apple does not provide support for Family Sharing of their AirTags.

Ref: What to do if you find an AirTag or get an alert that an AirTag is with you - Apple Support

By default, an Apple iPhone will have "Find My Network" enabled. This feature (along with Bluetooth being enabled) will allow the iPhone to receive the AirTag's Bluetooth location signal, and then in turn, transmit that location (encrypted) to the Apple servers to be used with the Find My service. That is how you would be able to see it on your iPhone in the Find My app.

I bring up "Family Sharing" as this may be implemented by Apple in a future firmware update to the Apple AirTags. This may be how to resolve the issue you are referring to here ... where family members would not be "affected" by your AirTag ... and vice versa.

In the mean time, here are your choices. None of these are ideal:

• For each family member iPhone, disable the "Find My Network" feature. Also disable Bluetooth.
• Remove the battery from the AirTag.
• Don't use AirTags. Look for another solution for why you decided to use them in the first place.

Alternately, you can contact Apple Support directly for assistance. To do so, simply select the "Support" link on the lower left-hand side of this forum's web page.

I believe the owner of the AirTag has to enable Family Sharing for an AirTag to be shared on multiple devices before IOS 17. The owner will also most likely have to add iCloud+ for more storage. Otherwise, others that are near the owner's tag that they didn't include in their Family Sharing will get the alert that they're being followed, and they can only pause it for 24 hours. After IOS 17 they can share the AirTags with up to 5 more devices. iPhone 15 or newer is required for precise location.

Actually, they do. I just got off the phone with Apple support and they said the way to stop getting alerts from a family member's AirTag is to share the AirTag. Go to the Find My app, then go to items, and find the AirTag. Tap on it. Scroll down to Share This AirTag. Click Add Person. Find the family member and select them. Now the AirTag is shared and won't give notices. If your family member shares their AirTag with you, you won't get notices any more.

That's because, as I mentioned, Apple does not currently offer the ability to share an AirTag with family members.