Thanks for your question and especially for posting the link to your screenshot; very helpful.
The “<- click to toggle” label is a bit confusing because the name of your custom taxonomy is long enough to make the label wrap to the next line. You should be able to click on any of the taxonomy names in the pane to load the terms assigned to the current item. Just click on the “Resource Categories” title – if that doesn’t work, let me know.
If you always want to see the assigned terms in the ATTACHMENT DETAILS pane you can bypass the “click to toggle” step. Go to the Settings/Media Library Assistant General tab and scroll down to the “Media Manager/Media Grid Enhancements” section. Look for “Media Manager auto-fill meta boxes” and check the box, then scroll to the bottom and click “Save Changes”.
I hope that gets you the results you want. I am marking this topic resolved, but please update it if you have any problems or further questions regarding Taxonomy information in the “Add Media…” popup window. Thanks for your interest in the plugin.