USB HDD on Raspberry or Wi-Fi modem router

I have an issue with my Volumio on Raspberry 2:

  • if I connect the USB HDD (with my music inside) on the Raspberry, I can see all folders and files (more than 100 folders and more than 2000 files), but the start-up is very slow, I cannot access the media files before 10 min at least;
  • if I connect it on my Wi-Fi modem router, Volumio can just see 15 folders and not all the rest.

The Raspberry is connected via LAN to the router.

Please help me to solve the issue, if there is any additional information you need, please let me know.