I have a strange issue. For the purpose of this experiment, I have been using my TB on WIFI for about 75% of the day for the past 5 days. In those 5 days I have been monitoring my data usage @ the VZ site. It looks like my VZ data counter is going up even while I am surfing over WIFI.
Hmmmm....how much of an increase. Maybe when you leave the house, the synchronization of Google and your phone requires more bandwidth over a wireless network (as in carrier) rather than your house. This is strange. Is it a vast amount of data increase?
Some Apps can't use a wifi connection, though that doesn't sound like what you are seeing. It may be a background application or your phone may be disconnecting from the wifi and switching back to mobile connection. Do you have a strong wifi signal? Does this happen as you are moving around? Is there another router nearby that's running on the same frequency causing interference, then a disconnect?
I use wifi at home and have kept an eye on the data and have not experienced what you are seeing. Can't answer about the rooting thing as I am not rooted.
Another thing to look at is under Wi-Fi settings, see if you have "Advanced" by pressing "Menu", Check the Wi-Fi sleep policy. Make sure you select "never". I don't know if stock TB has this or not, but with CM7 ROM, it does. If you don't choose "never", then Wi-Fi may turn off, and 3G/LTE/1x may run instead. Otherwise, you may be running applications that don't use Wi-Fi or you have a very weak signal.