If you simply expanded the archive into your Q2A root everything should have been taken care of. In other words, there was no need to rename any directory. The "qa-external-example" directory can remain as is.
OK, then, in your "qa-external" directory you should have two files:
qa-import-tags.php
tags.txt
Do you have those?
And you should have replaced:
<site-root>/qa-include/qa-page-ask.php
<site-root>/qa-include/qa-page-question-post.php
with the new versions.
Did that happen?
If so you should see tags from tags.txt appear as you type tags into the Tags textbox of a new question. To be clear, this mod does not add tags into the database at all. You will not see these tags in the "Most popular tags" list unless you actually use them in questions. Maybe that's the issue?
BTW, I'm running 1.5.3 and know nothing about any prior version.