Once you have mounted the Sparse Image, it will appear as a drive in the device list in the sidebar of the Finder. Select the device in the sidebar. If you can navigate to the Backups.backupdb folder and then to the correct drive, you should be able to see your backup files. Select a date and wait a few minutes. It make take a minute for it to populate the files depending on the speed of the connection. If no files appear, then the backups may not have occurred.
In addition: You should have a spinning wheel at the bottom of the window in the progress bar (if you enabled it to show) while it is accessing files.

I don't really know about the drive you are using for backup. In the past, it was not recommended to use any other NAS other than Time Capsule for NAS. However, things may have changed and some may now be usable. You would have to check on that with your particular drive.