Since the release of the iPhone 5 and iOS 6, some Verizon customers noticed that their devices were still consuming their expensive cellular data minutes -- even while their iPhones were on a WiFi network. Apple has released a carrier settings update for the Verizon iPhone 5 that resolves the issue.
Carrier settings update 13.1 may be installed by users who have not received notification on their phones by following instructions posted in Apple's support knowledge base. Verizon iPhone 5 users should tap Settings > General > About, and wait for an alert to appear. After tapping OK to install the carrier update, users are instructed to reboot their devices by holding the sleep/wake button down until "Slide to power off" appears, and then use that gesture to power off the iPhone 5.
Once the device has been powered on again, users are instructed to verify that the installation was completed correctly by once again tapping Settings > General > About, and checking Carrier to see if "Verizon 13.1" is installed.
Thanks to @RColwell for the tip.