This one had me scratching my head for ages, and it was only some good investigation by @domsoar that found the answer, here: http://thenorthernedge.ca/blog/how-customize-addthis-for-your-website-or-blog-3559/.
The answer is to use a custom button and this sort of code:
<div class=”addthis_toolbox addthis_default_style “>
<a class=”addthis_button_tweet” tw:via=”YOURHANDLE” tw:related=”YOURHANDLE “></a>
<a class=”addthis_counter addthis_pill_style”></a>
The bit that actually fixes the ‘via’ reference in the Tweet is emboldened above. I had tried with the ‘via’ reference previously with no success, but the tw:related argument fixed it!
Hope this helps someone 🙂