No there is no data charge for messaging.  The cost of the data that MMS message use is included in the price of the message (pay-per-use or messaging plan).

What your seeing is regular internet usage.  When your phone connected to the internet for message anything else on the phone that needed data would have been able to transfer at that time.  It can also be a coincidence at data is not alway reported right away so data at that time could have actually been from an earlier time.