I got (very quick) response from Tt support. They confirmed that the fan speed can't be controlled by the MB, these fans turn at constant speed. Ouch!
I was actually very happy with this chassis, it's well built, fair priced, has proper cable management and it looks very good. However, I had never expect that the fan speed isn't controllable. The whole advertising conceals this important fact. Even the manual suggests to use the Tt RGB Plus software. So my advice is, if you consider buying this case, buy it without the RGB fans and put 'real RGB fans' into instead.