Cellular data OFF

I have travelled a few times this year, and I have purchased from Bell in Canada the "Roaming Better" package. Basically, if I use my phone when roaming, the "Roaming Better" package is triggered and for the day I am being charged $10. For that $10, I can then use my phone for that day only (data and voice). However, to avoid being charged if I do not need the phone, I set my "Cellular Data" at OFF and my IMessage at OFF, and do not answer any calls coming in. However, it has occurred a few times where Bell claims I have exchange data and they have charged me that $10. How could that be if the cellular data is at the OFF position including IMessage being at OFF??? Is this a problem with my Iphone basically, as Bell claims there has been data exchanged between my phone and their network ??