I'm not aware of any cable companues putting bandwidth notices on customer's TVs but if you are seeing that, I assume you don't have unlimited bandwidth. It's something you should talk to your cable company about.
If you stream movies on Netflix, Amazon, or anywhere else, a 2 hour movie eats up about 2-4GB of data. A lower tier plan from cable providers usually only include 100GB per month. On top of that, iPhones are notorious for eating up 8GB-64GB of data every time you plug it in to power and it does its daily backups.