I have noticed that available instructions for configuring Volumio to work with the HiFiBerry board are a bit outdated here, so for anyone trying to make Volumio work with the HiFiBerry, these are the steps which need to be taken:
1. Go to the Playback menu
2. Under the Audio Output drop-down menu, select the sndrpihifiberry option
3. Go to the System menu
4. Under the I2S DAC drop-down menu, select the appropriate HiFiBerry board model
5. Apply changes and reboot the Raspberry.
This applies to Volumio release version 1.55, latest Volumio release at the time of writing this post.