Hi Robocuc2,
It should be noted that Blackberry also heavily compresses it data that streams to the device. This is part of the Blackberry Internet Service. It's not uncommon to see your data use go up switching from a Blackberry to an iPhone/Android or Windows Device.
The visual voicemail feature on the iPhone (as well as most newer Android phones) uses small amounts of data during the day to check for new voicemail so this would account for your tiny data transactions you see on your account.
Data calculation is on a delay for posting in the billing system of what you see, usually 12 to 16 hours which is why you would see data usage thoughout the day and at times when you say your data is shut off. It's when the system posts it, not necessary when the data was used.
Hope this helps!