Hello dheidle,
Because your kids signed in to their new devices with their own Apple ID the Apple Care One coverage will cancel within 24 hours of receiving the email because the coverage is under your Apple ID NOT theirs. Coverage can only apply to one Apple ID.
I had the same experience this Christmas buying my Wife an Apple Watch and I signed up for Apple Care One at the same time. I added two other Apple devices so as to have 3 total for the price. Come Christmas day my wife opens up her new Apple Watch and in the setup process assigns HER Apple ID to her new Apple Watch with her iPhone.
I get the same email warning message you did.
After chatting with Apple Support my only option was to get the AppleCare+ that only covers one device under her Apple ID. for her new watch. I removed the coverage for her under my Apple ID and added another device I have. Problem Solved.
AppleCare - Apple