Hey Max,
I saw your messages on #lwjgl earlier and have already fixed this. Try the next nightly build.
The main problem was that the worker context has to be created/shared on the main thread and then made current in the worker thread. Creating the context in the worker thread was working fine on AMD, but failed on NV and Intel. I've also improved context synchronization; on NV's multithreaded driver you need to explicitly sync the two contexts, otherwise the GL commands get mixed up and everything behaves weirdly. The demo will now use fences (OpenGL 3.2+) for synchronization and fall-back to glFlush if they're not available.