Thanks for your interest in the plugin and for this question. The incorrect counts is a problem I noticed early on and addressed in one of my FAQ entries:
Why don't the "Posts" counts in the taxonomy edit screens match the search results when you click on them?
This is a known WordPress problem with multiple support tickets already in Trac, e.g., Ticket #20708(closed defect (bug): duplicate) Wrong posts count in taxonomy table, Ticket #14084(assigned defect (bug)) Custom taxonomy count includes draft & trashed posts, and Ticket #14076(closed defect (bug): duplicate) Misleading post count on taxonomy screen.
For example, if you add Tags support to the Assistant and then assign tag values to your attachments, the "Posts" column in the "Tags" edit screen under the Posts admin section includes attachments in the count. If you click on the number in that column, only posts and pages are displayed. There are similar issues with custom post types and taxonomies (whether you use the Assistant or not). The "Attachments" column in the edit screens added by the Assistant shows the correct count because it works in a different way.
This is still an issue; Trac ticket #14084 has attracted 32 comments, the most recent on 3/2/2013. I haven't been able to reproduce the problem in a controlled way, but I'm confident it is not related to the MLA plugin. I wish there was a better answer, but the fix will be in WordPress, not the plugin. For that reason, I'm going to mark this issue resolved.