As the name states the basic composition with these type of courts is that they are built on top of asphalt. Asphalt makes for a very stable and very level surface. However, asphalt is very hard and is generally tough on a players ankles, knees and back. To help reduce the hardness we can add multiple layers of granularized rubber over the surface. The coats of rubber are added in layers to eventually arrive at anywhere from 3-10 coats. The more coats, the softer the surface becomes. The ultimate effect of the rubber is that it provides some compression under foot. You still are not able to slide but you are playing on a surface that gives a little thereby helping with back issues.
Cushioned asphalt courts require very stable sub-bases with absolutely no sub-surface water issues. The rubber typically will lose its cushioning feel when temperatures get below 40 degrees. However, due to the courts requiring no daily maintenance, their softer playing surface and the fact they can be coated and colored to almost any look, these courts are very popular at major tournaments, colleges and clubs.