I have the exact same problem!
I'm using the iPhone 5 now under Carrier M1 Singapore 13.0 and I have noted that over a period of 2 weeks, my cellular data usage has been about 2.7GB on an average. Since I know my bill has been capped at 3GB, I have since switched off my cellular data.
However, when I switched it on for a few days after using it for awhile, my cellular usage jumped by 1.2GB in just 1 day! And I used it as I would on an average day (like during an average day in the 2 weeks)!
I understand that there have been reports of a bug that have caused this problem in the US.
http://www.technobuffalo.com/companies/apple/iphone/verizon-iphone-5-cellular-fi x/
http://www.iphonehacks.com/2012/10/iphone-5-cellular-data-usage-over-wifi-bug-on -other-carriers.html
But I'm hoping that there's a solution for those living in Singapore? Do I seek the help from my carrier as well? But if it's a problem with the phone, then my carrier definitely would not help, right?