When does macbook second HD work?
Every time an application access a files on the HD, it will start itself. Sometimes it can be a background process who does this, that's why it may happen although you don't access a file directly. 

You can watch this with this command : lsof | grep "/Volumes/HDName"

lsof lists the files accessed by the all process. The grep selects only the files located on the HD. 

If you want to stop the hard-drive, just unmount-it.