My issue, which shares your subject heading, occurred today and several days after a seemingly normal update of my iPhone 5 to 9.0.2.
Issue: Wifi became unavailable and phone started using LTE data while streaming video without my knowledge. Wifi was working normally on other devices so this was not noticed until the carrier sent a text informing me that my LTE data monthly limit had 200MB of my 2.5GB remaining with 25 days left in my plan.
Visual clues: RF signal was showing 2 dots +"AT&T LTE", normal is 2 dots + "AT&T", and a wifi full strength indicator.
Remedial steps taken: Manual sync with wifi didn't work and no DHCP lease issued. Don't know if network name shown was because phone remembers friendly access points or if the radio was actually on.
Going to Airplane mode and turning on WiFi had a similar result.
A normal reboot, turning phone off and then on, brought the phone back to normal operation.
Since my normal cellular data usage is about 250MB per month this has caused a temporary behavioral change including going through Settings and disallowing on every app the new to iOS 9 feature; Allow Cellular Data.
I've a road trip in a few days so I'll have to add data to my plan at the ridiculous AT&T rate of $20 per GB.
