I got the toolbar, eventually. The test user had last logged into the main site before DST changed, which means that the site will try to internally redirect to a page that changes the DST setting. However, your wiki.subdomain is not included in your site's referrer whitelist, so the POST to the non-wiki.subdomain was rejected and this caused a number of items that require POST submission tunneled to that domain, including the editor toolbar WYSIWYG activation, to be broken while viewing the sub-domain.
Once I simply visited a page on the main domain, the DST setting reset, and returning to a wiki page and the editor loaded the WYSIWYG toolbar as expected. To avoid this issue for other users, I would add your wiki sub-domain to your site's referrer whitelist (in vBulletin's settings, and also vBSEO's settings if you use that product).