There seems to be quite a lot of confusion surrounding the TypeScript support in Visual Studio 2013, and I believe that is partly down to how the tooling was previously implemented in WebEssentials.
As an early adopter of TypeScript in Visual Studio 2012 using Web Essentials, the development experience was pretty self explanatory.
- Add a new TypeScript file
- Edit (with nice preview window) and Save
- WebEssentials would generate a .js and .min.js file and automatically add them to the project
When moving to Visual Studio 2013 I was looking for the same functionality from the integrated plugin but found little success. However after much frustration I eventually figured out the differences between the tooling, and I now happen to think the plugin is actually better than the WebEssentials implementation (excluding the lack of preview window!).