Support

Actually, that's not accurate. All your images are linked to the HTTPS site. I analysed all 144 resource requests on that page myself. The only problems I see are:
- External resources (e.g. the LinkedIn logo) are linked to the HTTP, not the HTTPS version of the external site. You have to manually link to external HTTPS resources, Admin Tools won't do that for you.
- There are 7 images which throw a 404. The URLs seem to be generated by Javascript on the page. THey all end up trying to link to an inexistent file called "-1" which makes me believe that some Javascript on the page got borked.
- All image links generated by Javascript are, of course, not converted to HTTPS. Admin Tools is a Joomla! plugins and operates on the HTML content of the page. Any image links generated by Javascript are generated in the browser, long after Admin Tools has finished running.

As far as Admin Tools is concerned, it does exactly what it is told and should do: it converts internal links which are present on the page to HTTPS. It doesn't deal with dynamic links created by Javascript and it won't touch external links. What you describe as template images is actually Javascript-generated image links, so you have to modify the Javascript file which generates them. Normally, the author of the template should have provided Javascript code which can detect if it's running under HTTPS and adjust the links accordingly.