Chromecast devices need to be connected to WiFi (with full internet access) to work.
When you cast from your phone, you actually just tell the Chromecast to go to that service (Netflix, Google Movies, etc) and get the stream directly from them. Your phone doesn't pass the movie.
There are ways to use a phone to supply the WiFi, but they are tricky and not officially supported by Google, and you often need ANOTHER device (phone or tablet) because most phones can't make the WiFi hotspot and also be on the hotspot to talk to the Chromecast device.
