Apple watch "family setup" owner can't send SMS from other devices

My child has an Apple watch with cellular service, but no iPhone. She also has an iPad and Macbook on the same iCloud account. She can send iMessages to other Apple-device owners just fine from any of her devices. She can send messages to Android users (via green-bubble sms text messages) from her Watch just fine as well. But she can't send Android users messages from her other devices. Is this expected behavior?