On motherboards prior to the Z77 chipset, literally *all* USB-3 controllers were 3rd-party.
USB-3 had not yet been integrated into the Intel chipset.
Using a 3rd-party USB-3 controller can indeed cause issues with many USB audio interfaces and MIDI controllers.
We've seen it countless times...
If you're running a Z77, Z87, Z97, Z170, Z170x, X99, or X99p motherboard (or derivatives), you're fine as USB-3 is integrated into the Intel chipset.
You implied correctly.

The USB controller can/does make a difference.
If you've got an older motherboard with 3rd-party USB-3 controller, the solution is to use the USB-2 ports (which are Intel). There's no performance advantage when connecting a USB-2 audio interface to a USB-3 port.
This is no different than talking about using a Firewire audio interface.
For maximum performance and compatibility, you want to use a TI chipset Firewire controller.
Same with SATA-III controllers...
Connect a current generation SSD to a 3rd-party SATA-III controller... and benchmark it.
Now, connect that same SSD to an Intel SATA-III port... and benchmark it.
In most cases, you'll find that the Intel SATA-III controller outperforms the 3rd-party controller.