Option #1 (and the first thing I would try):
Clear 'Default' Music App in App Settings
Alternatively, visit Settings > Apps > Specific Music App that is default now and clear it as default
Uncheck 'Play Music' from 'In App' in Google Now Settings
Open your preferred music player and make sure it is able to successfully play music from your SD Card
BEFORE setting this as your default music player, say the voice command, 'Okay Google, Play Specific Song/Artist On Specific App'
If it asks you to set this app as your default... do so, if not...
Go to Settings > Apps > New Default App and try to set it as default music player
Then try to say another voice command such as, 'Okay Google, Play The Beatles' and see if it works.
Option #2
You can actually upload your music files directly to Google Play Music which will then allow you to access the songs through the app or anywhere you have Google Play Music.
You will likely then have to open the Google Play Music app on your phone and choose to save certain files to your Micro SD card for playback, which seems tedious, but I believe it will work. Note: haven't tried this myself.
Here are the instructions:
https://support.google.com/googleplay/answer/1101500?hl=en