There are two microcontrollers on the NeXTUSB, there's one file for each of them.
Place one file (not both) on a FAT-formatted USB flash drive and plug it into the NeXTUSB while it's running. Make sure the file name stays the same.
The red LED in the device will flash 4 times and then wait 5 seconds to begin.
If updating NEXTUSB.ROM, the red LED will flash very rapidly while updating. Once it stops, remove the flash drive. Press the reset button on the device.
If updating NEXTUSB8.ROM, the red LED should flash 4 times rapidly when it succeeds. It may take two or three times to finish, so let it repeat the process (flash slowly, wait 5 seconds, wait for rapid flashes) until it succeeds. There's no need to reset the device after updating this controller.