The phone doesn't update itself unless you tell it to. So the "feature" is always off, till you tell it otherwise.
Same goes for all the apps. The App Store app will pop up a red number telling how many apps need updating, but until you start it, tap the Update icon and Update All (or each individually), NO updating will occur.
So if you find yourself at the edge of the data usage precipice, the phone is totally innocent.
Beware the 6.1 update if on a tight data plan. The file containing the OS is a tad over 1GB in size. Then there's the mandatory iCloud backup before updating really begins if you do it OTA.
Much safer and cheaper to plug it to a computer and let iTunes do the heavy hauling over your Internet connection. I recommend selecting local storage for the backup; much quicker and a lot less work for the phone.