Thank you for uncovering not just one, but three MLA defects which I have now fixed. You get the award for testing out the "Edit Tags" screen!
First, you reported incorrect Attachments column counts. I have fixed a defect in the SQL query the plugin uses to get the counts (and I improved its performance as well).
Second, you noticed and reported the odd "Quick Edit" behavior. The changing count and alignment happened because the plugin's code for the Attachments column was never called; the update came from the WordPress Posts/Media column handler. I've fixed this as well.
Third, the left-aligned Attachments values have been changed to center-aligned; the same style used for the Posts/Media column. Not a defect, exactly, but cosmetics count.
Your "Alternative solution: use the plugin 'Attachment Taxonomy Support' from Ben Huson..." does not solve the problem. It replaces the MLA Attachments column with the WordPress Posts/Media column, which does NOT report the correct figures in all cases (see the MLA FAQ page for more information).
The only real solution is the set of fixes I've just completed. The defects have been in the plugin since version .30, and you're the first person to report them. Since the defects are relatively harmless, I'm going to hold off on a new release for a while and see if anything else comes up.
If you want to get an updated version and try it out, send me your e-mail address and I will send you the latest code. Go to the "Contact Us" page at our web site:
Fair Trade Judaica/Contact Us
Thanks for your excellent reporting, your patience and for using the plugin. Thanks, too, for the link to "Admin Management Xtended", which looks like another great plugin.