I bought a Turbo-X branded PCIe USB3.0 controller, because I don't want to spend money on a new computer with USB 3.0, but I have a few devices which can benefit from that.
The price was quite reasonable - around 13€.
I mounted the board, and Windows 7 issued an error that there is a problem with the installation. There was a small CD with the package, and I installed the driver from the CD.
Several restarts - there the problem remains, and the device stays yellow in the device manager.
At least from the TXT file on the CD I could find out that the board is based on Renesas uPD720202 chip. So after that I could find some good people on google like here, where I understood that I am not alone, and a lot of manufacturers use this chip.
The problem was connected with the chip firmware, it needs to be updated. Unfortunately the link mentioned in the forum above does not show directly the necessary software. You can see it HERE, and I chose the last version "Controller Firmware Version 188.8.131.52".
If there is a newer version, maybe it is better to download it. But be careful, some of the links are not for uPD720202, but similar, and some of them are drivers, others are firmware.
After installing the firmware update - one button click - and restarting the computer, everything worked like magic.
14.12.2016 - P.S.
To summarize things I put 2 download links from my hosting, to make sure these rare files are available. I lost the CD with the drivers, and Plesio was not able to help me.
Drivers - LINK
Firmware - LINK
Original TurboX driver from CD (looks the same) - LINK