I did a quick search on Google, and all I could find about their software and Linux was someone's GitHub project that appears to be their own software for controlling the fans. However I don't see support for the Riing Trio fans listed. The owner appears to be taking requests to add products, but there is no guarantee.
https://github.com/chestm007/linux_thermaltake_riing
Another member on the forum has written their own software as well, but I am unsure if it has Linux support. They are working on Riing Trio support, though.
Thermaltake's support is terrible. Purchasing their products in the hopes that someone else's software will get you what you want may be a large gamble. You could try ordering off of Amazon, as they are usually great about returns. Then you can send things back if you can't get it working. Otherwise, I recommend looking elsewhere.