Updating the drivers is easy. All you have to do is download the file below
http://station-drivers.com/telechargement/asmedia/asmedia_usb3_1.16.1.0allos(www.station-drivers.com).exe
It's a self extracting archive so extract it to the default directory (usually Downloads) with an arbitrary subfolder. Make sure you add a subfolder to the extraction path. If you do not it will clutter your downloads folder.
Go into the subfolder and run setup.exe. Follow the prompts and it will install the drivers
Updating the firmware is much more difficult. ASMedia hasn't made it possible to update the firmware through the driver interface and instead must be updated through an operating system which does not have a hardware abstraction layer.
To get started with flashing the firmware you will need three things
1. The HP USB Disk Storage Format Tool. This will allow you to format a USB mass storage device into a bootable disk. It will also let you install the DOS compatible FreeDOS kernel and command interpreter which you will use to flash the firmware. Get this from here
http://files.extremeoverclocking.com/file.php?f=197
2. The FreeDOS kernel and command interpreter. These are literally only 2 files. Grab FreeDOS 1.1 from here
http://www.freedos.org/download/
It's an ISO but you don't want to burn it. Instead either extract it using WinRAR or mount it using any ISO mounting tool.
3. The latest firmware for the device
http://station-drivers.com/telechargement/asmedia/asmedia_asm104x_12220E(www.station-drivers.com).exe
Now that you have everything ready, grab your USB stick and prepare to wipe it. It will be reformatted so back up anything that may be on it.
Run the HP Disk Format Tool. Select the appropriate device if it is not selected by default and check "Create a DOS Startup Disk". For the field below which says "Using DOS system files at..." point it to the extracted/mounted FreeDOS installation CD and into the subfolder "FREEDOS/SETUP/ODIN". The subfolder is very important, it will yell at you if it doesn't find what it's looking for.
Press Start. It will only copy two files and they will both be flagged as protected system files on the USB stick so you won't see them unless you have those shown; if you see what looks to be an empty disk don't worry.
Extract the firmware from part 3 above into a subfolder on the USB stick.
Reboot your PC and press whatever key you have to press to get into the boot menu (usually escape or F8 on Asus motherboards). Select the USB stick rather than the hard drive. If the boot menu is organized it may show up under Hard Drives or Removable Devices.
If you're not familar with the DOS command syntax you may want to get familiar with the Windows cmd.exe first, it has the same syntax as the DOS command parser. All you'll need to do once you're in FreeDOS is change directories and run a batch file.
To change a directory type "cd DIRECTORY_NAME"
To change to the directory immediately above the current directory type "cd .."
To run an executable or batch file (.bat) just type the name
Once you're in FreeDOS change into the subdirectory that you extracted the firmware to and run "u.bat". It should do the rest automatically.
Once the updater has run you will be returned to the command line. You are now done and can reboot the PC
good luck