This was followed by a dialogue with Inateck and support of Gigabyte. On their advice, I plugged the card on a PCI-e 16X connector (yes, it is compatible despite the size difference between male and female connectors), and everything started to work with my external drive MyPassport 2TB USB3.
I recommend this card, and especially since the Inateck proactive support is to emphasize (Alice thank you!).