Apple Watch Question

I’m trying to figure out this situation: I was wearing my series O Apple Watch at the gym. My iPhone SE was at home. During my workout I received a text. My phone at watch were not connected together due to distance. The Apple Watch did connect itself to the gym WiFi. Is that enough for the phone to receive and send a text? The settings for the phone have the “use WiFi when out of cellular network “ disabled. Give this is a series 0 watch, I’m both puzzled and impressed. When I got home after the workout I was informed that my phone had been “ringing” with message alerts, so I am sure the phone wasn’t even remotely close to the watch while I was at the gym.

I think I read a while back that if both sides were connected to WiFi this would happen but haven’t ever tested. Think from memory it came in with iMessage in the cloud.

The Apple Watch automatically connects to wifi it “knows” that only requires a password (not login portals or enterprise networks with usernames and passwords), then through the wifi connection it can receive messages, both SMS and iMessage, the former only when “Messages” is enabled in your iCloud settings.