An Apple support page details a fix for an apparent issue involving cellular data being used while connected to a WiFi network. Verizon has stated that incidental traffic will not be billed to users, however, Verizon iPhone 5 owners will want to make sure they have the latest carrier settings.
The following directions from Apple assists users to ensure settings are updated and installed:
This carrier settings update resolves an issue in which, under certain circumstances, iPhone 5 may use Verizon cellular data while the phone is connected to a Wi-Fi network. Follow these instructions to install the update.
Tap Settings > General > About.
Wait for the following alert to appear: (See graphic)
Tap OK to install the update.
Hold the Sleep/Wake button down until you see "slide to power off".
Slide to power off.
After the device powers off, hold the Sleep/Wake button to turn your phone back on.
Note: To finish the installation of the update, your iPhone 5 must be turned off and then on again.
After your iPhone restarts, tap Settings > General > About, then scroll down to Carrier and verify that "Verizon 13.1" is displayed.