It is converted, while you’re processing, to be displayed. Internally, the software works on a high-bit-depth image that has gamut corresponding to the chosen working profile. But when that image is to be displayed, its converted to whatever bit-depth is handled by the display, and the colors are crunched down from the working profile gamut to the display gamut. This happens (mostly) every time you make a change: add a tool, or change its paramters. Otherwise, you’d be looking at colors that look like the first image I posted previously.
There’s a diagram in this article that might be helpful: