There are two modes. In “Standard” mode unconverted images are redirected internally to the converter, which converts the image and serves it as webp. The generated webp is stored. The next time the jpg/png is requested, it will be redirected directly to the webp – a .htaccess rewite rule takes care of redirecting to existing (for browsers that supports webp).
In the other mode, jpg/pngs are not redirected to webp. In that mode you must currently use another plugin for altering Html. However, in the next release, WebP express will be able to alter Html. It will support both picture tag syntax and replacing the image urls directly (for browsers that supports webp). I expect to release it in the middle of next week week. The next release will also have a feature for automatically converting a webp when the webp is requested but missing.
There is no need to copy images or to know when all images has been converted. Each image will be converted the first time it is requested by a webp-enabled browser. I have bulk conversion on the roadmap, but as it isn’t really needed, it is further down the road