What USB chipset is used in this? (I'm wondering if it would work on an old Mac Pro 5,1 with a modern OS, as some of the USB chipsets were broken after Yosemite)

Hello, This adapter card comes with the Renesas uP720201 chipset. We don't know if it's going to work for you with your equipment involved.  It seems like it should work but it's hard to know for sure. All modern OSes come with built-in USB 3.0 support, so the driver should automatically install when the card is installed.