Apple has rolled out iPhone 5 (Verizon) Carrier Settings Update 13.1 which is an important new carrier settings update is now available for iPhone 5 on the Verizon Wireless network.

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.

To install the update:

1. Tap Settings > General > About.
2. Wait for the following alert to appear:
iPhone 5 carrier settings 13.1
3. Tap OK to install the update.
4. Hold the Sleep/Wake button down until you see “slide to power off”.
5. Slide to power off.
6. After the device powers off, hold the Sleep/Wake button to turn your phone back on.

After your iPhone restarts, tap Settings > General > About, then scroll down to Carrier and verify that “Verizon 13.1” is displayed.

More info via here.