Be sure and check the shock absorber on the belt tensioner whenever you have alt pulley issues!!!!!!!! I went through 4 pulleys and an alt on my first experience with a bad one. The defective shock allows a vibration to be set up in the belt and causes the pulley to fail.. or maybe even loosen up.

If you have access to an impact wrench.. that will sock the nut down tightly, and is the best way to do it. If not.. then you need sockets that are open to insert the allen key into to hold the shaft tight while you tighten nut.

I assume of course you have a serpantine belt as opposed to the double V belts?