I'm not sure this solves your problem but you do need to specifiy the location of the iTunes music library if you want it stored somewhere other than the default, which would be the internal drive on you iMac.
Open iTunes and select 'Preferences' under the 'iTunes' menu at the far left of the menu bar on your iMac. Then click on the 'Advanced' icon at the far right in the Preferences dialog box.
The top box shows the current location of your music library, probably something like, "/Users/yourname/Music/iTunes/iTunes Music. If you want it elsewhere click the 'Change...' button and navigate to your external hard drive.
Here's more detail from the Apple support pages. http://support.apple.com/kb/HT1391
Open iTunes and select 'Preferences' under the 'iTunes' menu at the far left of the menu bar on your iMac. Then click on the 'Advanced' icon at the far right in the Preferences dialog box.
The top box shows the current location of your music library, probably something like, "/Users/yourname/Music/iTunes/iTunes Music. If you want it elsewhere click the 'Change...' button and navigate to your external hard drive.
Here's more detail from the Apple support pages. http://support.apple.com/kb/HT1391