My son’s Apple ID is sending me texts from his Apple watch

My son has a iPad with his Apple ID signed in. I have a contact in my phone for his tablet called “name tablet”. He recently got an Apple Watch with his own phone number. I set up a different contact as his full name to differentiate the two. I sent him a message to his watch while he was at school. It doesn’t appear that he seen it but he started texting me about something else and when I got his message it came from the “tablet” contact and not his watch…. Is it because he’s not on WiFi?