The Corsair AF120 Quiets operate from 7V-12V - if you use the Bitfenix adapter, which is a 7V adapter, then add in the step-down adapter that comes with the fan, it's going to take it below the minimum voltage. Additionally, the way the Bitfenix adapter works is by connecting the 12V power line to the 5V instead of to a ground - this works (it's called the "7V trick", but if you don't have a high-quality PSU, it may sense this as a fault and shut down.
There are a couple of options that would probably work better, depending on what motherboard you have and where you're planning to use these fans in your case (exhaust, intake, both):
1. Skip the adapters completely, and hook the fans directly to your mobo. Use voltage control either through BIOS or fan control software to control the speed.
2. Use just the Bitfenix adapter to run the fans at their lowest speed. This will work best for exhaust fans.
3. Use an aftermarket fan controller.
4. Use larger fans (140mm) with any of the control options listed above - you can run larger fans slower for the same airflow and lower noise levels.
I could keep going for a while. Let us know what your build is and what exactly you're trying to accomplish and we can give you more specific recommendations.