Support

We have been using HTTPS since 2010 and, of course, we see images in all of our components. There is no issue with HTTPS compatibility in our software. And before you ask, yes, our site is also running on Joomla! 3.6.5 and PHP 7.0 just like yours and we do use Admin Tools 4.1.1. Moreover kindly note that Admin Tools is developed on an HTTPS local development server running the latest Joomla! release (currently 3.6.5) and the latest available version of PHP 7.0 (and 5.4, 5.5, 5.6 and 7.1). We've even published the Vagrant box we use for development.

I suspect that the problem is with the server setup. Just because the SSL certificate is valid and dynamic content (.php files) is served correctly it doesn't mean that static content (CSS, images, Javascript, ...) is served correctly too. I had some very interesting issues setting up SSL on the local dev server :) The other thing that could have gone wrong is either missing files or wrong permissions which would easily be the case if your host had to transfer your site to a different host / container / VPS to install the SSL certificate (pretty typical since most hosts have to give you a dedicated IP to install an SSL certificate). Since that'd be a server issue I'd recommend contacting your host.