Yes. If the owner of the tag is in proximity it will relay off the tag and not alert other devices around. This stops annoying things like driving passed someone and it alerting them about proximity, walking in public and alerting everyone. If the person leaves proximity after a while it will alert to let you know in case someone was following you and is no longer there. It’s not going to be immediate if the relay is in proximity, as like you and your mother, there can be a legitimate reason for it being there.

Makes sense if the owner is with you, that it wouldn’t notify until they are not with you.

That second sentence is why they’re stealing children