"TV everywhere" is a joke( "everywhere" means on your home connection only). Very little works if you're outside of your house.
Maybe only the local channels...
"TV Everywhere" refers to all the TV apps that are accessible, not just the TWC TV app. If all the networks gave TWC permission to stream their content through the TWC TV app, that would be more convenient (for the TV provider as well as the customers). However, that would mean basically that individual network apps like, ABC, freeform, etc, aren't really necessary anymore. When you try to use any network app--to get full access to all content you have to have a subscription with a TV provider anyway.
Same thing goes for any other TV provider.
What is the point of having the APP to watch tv if you have to be connected to your home WIFI, if i'm at home i will just watch on the TV. APP is pretty much useless