Just a word of caution, and just sharing something that I learnt from watching someone else's renovation, and personally witnessing a ceiling which had been built up and then torn down.
Firstly, most local contractors are NOT familiar with room treatment. They need guidance from an expert, or from yourself if you know what you are doing or have some experience in this.
Second, the usage of Rockwool extends beyond simply stuffing it into the false ceiling, feature wall etc. The material used to construct these matter. Many contractors will use aluminum or metal structs, which are lightweight and easy to install. These will rattle tremendously and no amount of rockwool will help.
Thirdly make sure they have attention to detail. Again, if they leave small amounts of debris, rocks or other material behind, such as in conduits, false ceilings etc, these material will rattle and drive you mad. So make sure they clean up and remove all these stuff.
I have previously posted on the use of wood, and also the need for reinforcement in the construction of the false ceiling and also the feature wall. In order to be sure, test it. I brought my 12" 500Watt SVS subwoofer to do a "shake, rattle and roll" test of my structures of my new place whilst the ceiling and wall were being built and we found all the potential points of resonance, as well and any areas prone to rattling and corrected them. It also helped me to illustrate the point as to why I was so fastidious about the details in preventing rattling.
Once everything is up, it is very hard to prevent and remedy it, so do it once, do it good.