As I understand it, audio compression reduces volume based on the compression ratio and threshold settings. For example, if we set the threshold at 10 db and the ratio is 4:1, the sound is reduced in volume by a factor of 4.
10 db divided by 4 db = 2.5 db
Our new sound only gets 2.5 db louder, instead of 10 db louder. That is a reduction in volume. It's because of compression that you can 'then' increase the output of the compressor back up to the level of the input signal. Therefore, the compressor compresses the signal, the overall volume drops, and then you bring the overall volume up.
I wonder if the Genos compressor automates both processes, making it "appear" that it increases volume? Is it designed to do the compression, and then automate the increase in volume instead of us having to do it manually? Hence, the end product is an increase in volume - counter to what VanRay describes. He's right, in that compressors do not increase volume - we do, after the compression has been done electronically.