Your TI based USB3 drivers are missing, and it is not clear why.
A clean install from a "system builder" DVD will not have those drivers and so you have to add them on afterwards. Make sure to get the ones from HP via the Z620 drivers sources. I'm using the ones they have there now, for clean installs, and they have been working fine. Don't get the drivers from another source. I believe there are more than one TI based USB3 driver chipset, and you want the correct one from HP.
If, however, you have done a "restore" of your Z620 build from the HP media then those drivers would be rolled in by HP already. Or if you are using your original HP install then how they got lost from Device Manager may never be known.
A quick install from the HP SoftPaq should fix this........ when you navigate to that you'll see a Driver-Controller (2) entry, and it will be in that folder. Version 1.16.3.0 from 2014. The installer is via SP65043, and it can tell if you are running 32- or 64 bit.
Here is what the two drivers should look like and where they will be in Device Manager:
