I’m surprised that a USB 3.1gen2 also sometimes know as USB 3.2gen2 (isn’t usb naming fun?) card would work on 10.9.5. At some point Apple added ASMedia chipset support to macOS even though no Macs ever shipped that use that chipset AFAIK. All 2012 and later Macs have USB3 built into the Intel chipset EXCEPT for the Mac Pro 6,1 trashcan which uses a server chipset with no USB 3.0 chipset support. That’s why 10.8.5 and above has FL1100 USB3 support as Apple added the FL1100 to support the 6,1 for USB3 support on that machine.
Apparently some USB 3.1gen2 cards pick up on drivers that work on 10.9 and 10.10 but only operate at USB 3.1gen1 (also sometimes known as USB 3.0, fun) 5gbps transfer rate. You do need at least OS X 10.11 El Capitan to get the full speeds.
Earlier I wrote that the Highpoint 1144D uses the FL1100 chipset so should work on 10.8.5 but that is not true, it uses 4x ASM1024A chipset and also requires at least OS X 10.9.0. However, the Sonnet Allegro Pro card definitely uses FL1100 and should work on 10.8.5. If you don’t need 4 independent controllers you could get a Sonnet USB3 card, or save some money and get a KT4004.