When you apply colour management to displayed images, the colours on the monitor or projector are affected but the underlying colour values of the clips' pixels are not changed.
The colour management for displaying images is based on the concept of Viewing Rules. These rules allow the system to apply the correct viewing transform for media tagged with a given colour space.
Note that the colour management is now applied not only to most viewports but also to preview windows, thumbnails, the colour picker, and many colour pots/swatches. (Although Sparks and the Stabilizer are now colour managed, there are still a few other legacy viewports that are not.)