On powering up EZ-USB, the core responds to the host's request with the default cypress VID/PID and the device enumerates as a cypress product. Once the loader driver has downloaded the vendors firmware, the device needs to let the host know of the new VID/PID, endpoint configurations and other descriptors specific to the vendor product. This can only be done by a temporarily disconnecting the EZUSB followed by reconnect. On reconnecting, the host will query the device again for its identity and the downloaded firmware should respond with the information specific to the vendor product. The device will now enumerate again (re-numerate) with the vendor product identity (VID/PID and descriptor). This process of re-numeration is indeed necessary when the firmware is downloaded by the host on power-up.
The only time that your firmware is not required to re-numerate is if you should do a 0xB2 EEPROM download of the firmware. In this case the device will load the firmware from the EEPROM on powered up and start running. This firmware (not the core) will respond to the initial USB request from the host, with the right vendor VID/PID. So a re-numeration is not required in this instance.