Howdy Gillowe,
Thanks for reaching out to the Apple Support Communities. We understand you have some questions about using a cellular network with your Apple Watch, and we'd be happy to help.
To get started, is your Apple Watch connected to your iPhone using Bluetooth or Wi-Fi when you see the Cellular button appear white? If so, then this would be expected behavior, and this information can be found in the "Related Article" that was shared on this thread under the, "Connect to a cellular network" section.
When your iPhone is not nearby, or when your Apple Watch is not connected to the iPhone using Wi-Fi or Bluetooth, you should see the icon turn green.
Also to send/receive messages from your Apple Watch, your paired iPhone would need to be powered on and connected to Wi-Fi or cellular, but it doesn't need to be nearby. For more details, check out this link here: Use your Apple Watch without your iPhone nearby - Apple Watch
We hope that helps.
Take care!