Why am I being charge for using data while I'm on Wi-Fi?

I just got a new iPhone 5 and I have been watching a lot of YouTube videos while on Wi-Fi with my cellular data is off and I'm being charged for watching all of the videos. I have I only used data to look up 1 thing and I have used up 2 out of 3 GB in 2 days please tell me why.

I'm on AT&T

Added (1). I have called AT&T and they did absolutely nothing.

Call them

If cellaur data is turned off you won't be charged

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