Delay mounting Backup Plus drive after being improperly ejected
There's probably a duplicate question here, but the system will run a filesystem check when the device attached is possibly a foreign file system or a native Mac filesystem where the journaling feature is disabled or the journal indicates possible failures of the disk allocation catalog or directory structures.

You can usually open Activity Monitor and see some activity start when you connect the drive while the OS is checking if the drive is correct before showing it in finder. Depending on size of the volume, this could take 5 to 25 minutes or more if the drive itself has hardware malfunction.

To diagnose this, you would need a tool to disable the disk arbitration framework and then time / examine the mount process for each disk that's out of the ordinary.


How to Disable USB Auto-mount
https://superuser.com/questions/531673/disable-auto-mounting-of-all-unknown-drives-on-os-x