Try following these instructions:
Compile-on-Save
I've been struggling to get my head around this too but I think I have it sorted. I think part of the confusion comes from the differences in approach between WebEssentials and the new TypeScript plugin integration.
I was an early adopter of TypeScript and used the WebEssentials tooling in 2012 to compile on save. I had this configured to generate .js and .min.js files, which were both added to the project automatically.
When upgrading to VS 2013 I was looking for the same functionality from the in-built TypeScript support, however it does not exist (as far as I can tell).
Instead I believe the integrated tooling in 2013 covers both development and production workflows.
The above instructions set you up for build time compilation which should occur during release. During development the "Compile on Save" feature generates the files on disk, but does not add them to the project.
I then realised the generated files don't actually need to be part of the project as they were before, and why it's better than the WebEssentials solution (excluding the lack of preview window!).