Some cards are okay without their external power connector hooked up, generally for self-powered devices, but this is "iffy" and many/most cards are not. Also, it looks like your card uses the VIA chipset. I've not seen anyone mention VIA chipset compatibility, and I suspect that Apple's MacOS drivers don't support it. I just searched the thread and found nothing.
So I speculate that you have two problems: (A) you've not connected power to the card's molex connector, and (B) it's not compatible with MacOS.
The safe bet is to return your card and get one of the recommended ones in the first post where someone has verified it works. This is what I recommend. Using a card with a chipset that's used by Apple in their Macs ensures current and future support in MacOS.
If you really want to push through with your existing card, which I do not recommend, then you can give the GenericUSBXHCI drivers a try. I think they support VIA chipset. If true, this solves problem A, but not well. Like all third party KEXTs, this driver may have problems with newer versions of Mac OS. Also you still have problem B, so you either have to hope for the best that the card doesn't need power, or you have to apply power.
Here is a link to the drivers. I did not look very hard. There may be something newer.
bitbucket.org