I am still stuck with this problem. I still wonder why the include plugin can provide a cache refresh but not the wst plugin - or where is the difference, because both would load the same file. As I have seen the difference must be in the handle, not in the render part, because the render() function solution given above is not working. My difficulty is that my PHP knowledge is very bad (I have worked in very different programming language environments before.)
The change concerning the rendering is too late. Something (loading of the included file) is happening earlier, but the handle part is not executing when caching is coming in.
I would be very happy to get some hints where I could look. In the meantime the only solution is to save the configuration settings - this causes to renew the whole caching for the relevant pages automatically and very easily. But it would be very inconvenient to be compelled to do this manually again and again. Should there not be any equivalent action or routine in the code of the plugin?