The best explanation for the data usage at unusual hours is delayed billing. Anytime VZW works with a 3rd party to gain tower access to an area they are subject to that 3rd parties data reporting capabilities. Sometimes that 3rd party does not deliver statistics in real time and bundles your usages into a few large sessions instead of several smaller ones. VZW consistently reporting usages at 4:00 AM certainly seems to fit that scenario.
However, HomeFusion is not a product that is normally sold in an Extended Support area or an area owned by 3rd party towers. Delayed billing should not be an issue for you. Perhaps VZW is getting its signals mixed up when talking to your device. You might want to perform the various resets on the HFRouter to reset its connection. I'd give VZW a call to get this scenario documented incase you get into an overage situation later.
If you have a connection log from your HFRouter then please post it for us to review. Perhaps we can find some more clues that will point you in the right direction.