A BIOS update will only update the BIOS that's currently being used on the card. So, if you want to update both BIOSes, then you have to run the BIOS update once, then shut-down the PC, switch the dual-BIOS to the other BIOS, then boot up the PC and run the BIOS update again, so that the second BIOS also gets updated.
If you only update one of the BIOSes for a dual-BIOS card, the other BIOS will remain untouched.