it shouldn't - unless you have WiFi turned OFF on your phone with Mobile Data on. if the phone cannot pick up your wifi signal, then it will hit your mobile data.
if you have an android phone, there are apps (like juice defender) that can make that switch for you automatically.
It took 2 or 3 customer service people to come up with the correct answer, but with the LG Revolution, it will switch to whichever signal is stronger. We have strong 4G, so if you walk throughout the house, even though you are on WIFI, the phone could switch to pulling data through the 4G if that signal is stronger.
So, the solution is that we had to disable the data download through the mobile network while at home, then re-enable when we leave.
I was very impressed with customer service, since they were trying to figure out what was going on. I was sent a customer satisfaction survey, and in my comments I said that it was a good thing I was tracking data usage the first weekend, since 2G each is more than enough when not on wifi. If I had not, I could have been hit with $100, $200 or more in data charges. I was not told, nor was it in any easily available info about this. Guess what!? Someone actually read the comments, and I received a call from a high up customer service manager. This manager was very glad I was watching this and that I had written that in my comments, since this is an issue they need to inform customers (especially new ones) customers about.