I'm having the same problem here as described in this old thread:
The interesting thing is that I have three websites on which this is working great but not on the forth, newly installed website.
Tried out everything described in the link above, nothing helped.
I checked the database and saw that the tweets are downloaded into wp_ak_twitter table. Interesting, so the information is there and just not displayed on the website when using the <?php aktt_sidebar_tweets(); ?> code...
Is there something which solves the problem?
Looking into Google with this, it seems that it is a very common problem which might require a fix.