The first thing you should look at before installing any type of wainscoting on top of tile is whether or not the tile installation is still structurally stable. If tile is installed properly, it will last a lifetime or more. It is easy to tell if the installation is going bad -- loose tiles, cracked grout and tiles that sound hollow when you tap on them are all indications of a faulty installation. Replace or remove those tiles before you add the wainscot.
Regardless of which type of material you choose for your wainscot, you need to ensure that you are using proper adhesive that not only sticks to the material of choice but also the tile. While most tiles will allow you to use most types of adhesives, some tiles such as polished granite and marble have such a slippery surface that they require specialty adhesives to keep your wainscoting in place.
When you are installing wainscoting on top of an existing tile installation, you may need to drill the tile at predetermined points so you can mount the new material on top of the tile. However, this is on a case-by-case basis because some wainscoting materials, like wood paneling or plastic paneling, can be glued on without the need for screws or mounting of any kind.
The only real downside to installing a wainscoting on top of a tile installation is that once you do it, ruins the ceramic tile installation for good. After installing the wainscot, you can never go back to the tile underneath because the wainscot will damage the surface of the tile installation beyond repair. If you ever decide you are tired of the wainscot, you will need to replace not only the new layer of wainscot but also the tile installation beneath to install your future wall materials.