Hi Jeremy... like I said I'm responding to your PM here so that the search function can do its job.
Posting a video was exactly the right approach here... yup, that's the classic "solid pulley bounce"... very noticeable at idle, particularly if your tensioner is old and/or has worn bushings.
It's caused by the momentum of the spinning alternator with its tiny pulley (so lots of leverage) fighting the normal pulsations of power delivery on a high-compression engine...especially at low RPMs.
You can imagine the pounding the crank sprocket key and crank keyway are taking as the belt loads and unloads. Over time this leads to the key and keyway degrading enough that the crank nose deforms, the sprocket wobbles loose, and ultimately if unchecked the engine timing relaxes to a point that pistons meet valves.

VW did in fact fix this issue by installing the clutched version of the alternator pulley on very-late AAZs and later in 1997 the early TDI engines. The clutch allows the alternator to free-wheel when it wants to overspin the crank sprocket... belt bounce gone.
Why didn't they fix it sooner?? My guess... it took 3-4 years (so from 1993 to 1996ish) before damaged cranks started to make their appearance.
In terms of what to do about it... lots of discussion here... your best bet is to let search be your friend:
1) click on the "home" icon at the top of the page... this ensures you're searching the entire board
2) in the "Search" window on the right hand screen enter "AAZ alternator pulley"
3) click on the "search" window to the right of the box
The first page of hits you'll get are very very relevant.... part numbers, installation thoughts, etc. Have a read and then post back if all of your questions aren't answered.
One other thought... one of the posts shows me drilling and tapping the alt shaft to install a back-up bolt against the alternator pulley as a safety. Given the way the pulley installs and how VW installs all their pulleys I'd not bother doing that again... doesn't hurt, but not really required.