Assuming it is the same phone and usage some causes include:
Stuck e-mail upload or down load
stuck app update
wifi not connecting correctly
i would go to settings/cellular and reset usage to zero so problem can be pinpointed to certain apps or system services.
then close all programs by double clicking home button and swiping up each running up
then do a reboot by holding down home and sleep/wake buttons for 10 seconds then let go.
Weth offered good advice.
You can also log on to your Verizon account and look at the details of your data usage. It will give you an idea of when the bulk of the data was used. This might help you figure out what caused the high usage.
To follow up on what Weth suggested, keep in mind that you can go to Settings...Cellular anytime and look through the list of apps to see which ones are using the most data.
While logging in is a way to see your data, it won't be accurately time stamped. Data used at 9:18am might not be reported until 1:13pm. This confuses a lot of people, especially as they use their phone in the evening and then complain "my phone used data at 1:22am, but I know I was asleep" - chances are very good they used it just before going to sleep.
These are the steps I took almost 2 years ago to throttle down my 5C data consumption. Read through the disccusion comments too, some good info exchange there.
Whenever I am not on a wifi, I manually turn cell data off. Since I don't need it when I am out and about. My phone still remains on stand by to receive basic txt messages and voice calls, which is all I really need my phone to do when its in my pocket.
You also should turn off location tracking services: Settings => Privacy => Location Services => scroll down to System services => scroll down to Frequent Locations => Clear them and turn this function OFF. The factory default is set to monitor and track your where-abouts, and yes it uses cellular data to accomplish this.
That is not typical. Mine comes up immediately, no delay. Did you try a reboot? (close all open apps, then home and sleep/wake button held together for 10 seconds then let go.)