Hi!
If you saw the "BIOS update [was] successful" message, it should theoretically mean it did update; however, because of what you describe, I'd recommend the following:
1. Reboot into BIOS. Once in the BIOS setup utility, press <F9> to restore BIOS default settings.
2. Reset any customized BIOS settings.
3. Clear all DMI event logs by setting the option to "Enable", which is located in the Configuration/Event Log section of the BIOS Setup utility.
4. Press <F10> to save the new settings and reboot the system, and see how the Operating System detects the BIOS version.