When you buy a new Galaxy S4, the phone will use 4G instead of Wifi (even if connected to both) as long as the bloatware/trialware callerID app is enabled. And yes, it counts against your data usage.
To prove it:
1) Turn off wifi and use the internet with 4G enabled. A good example is the Facebook app.
2) Turn on the wifi, wait for it to connect, then keep using the app. You'll see the activity lights on the 4G continue to run and very little activity on the Wifi.
3) Turn off Mobile Data and you will see the app now correctly uses wifi.
To fix it:
You must clear the data from and then disable the callerID app.
1) From the home screen press Menu --> Settings --> More --> Application Manager
2) Swipe to the right until you get to the "All" screen.
3) Scroll down until you find the app named Caller Name ID
4) Touch Clear cache
5) Touch Clear data, agree to clear it
6) Touch Disable
You can now go about your business and the phone will correctly switch between wifi and 4G.
This is an extremely dangerous bug as it WILL COST YOU MONEY if you go over your data plan, thinking you are on wifi.