I've had the Zmodo app running on my Nexus 5 for the last 24 hours with cellular data restricted for the one app. Here's what I observed:
While at home with Wi-Fi turned on, everything works great- including motion detect alerts and an indication that someone has rung the Greet doorbell.
At work, with Wi-Fi turned off, I do not get notifications of motion or the doorbell being rung.
If I open the app I can see the Greet's live view.
Data usage has dropped to almost nothing.
Battery usage is so low that the app is not included in the list of apps (meaning less than 1% battery usage)
It looks like this is a big step toward diagnosing the problem. Now if it were only possible to find a happy medium on the data and battery usage...
I would be more than happy to collect any additional information you may need. I'd also be interested in testing any possible Beta releases. For now the Greet is not very useful since I have to have Wi-Fi turned on to get notifications. Looking forward to getting resolution on this!