I had a similar problem when initially converting to a TypeScript project. I also set resolveJsonModule: true and the src directory was copied to the output dist directory.
The underlying reason is that one of my source files required package.json at the root of the project. Once I removed that, tsc no longer added src to the dist directory.
In short, make sure you are not requiring files outside of your src directory.
Explanatory FAQ here: https://github.com/Microsoft/TypeScript/wiki/FAQ#why-does—outdir-moves-output-after-adding-a-new-file