Even after setting up your magento to use HTTPS on the admin, the initial non-secure HTTP request to the frontend might need to be redirected to HTTPS.
You can force HTTPS on all incoming traffic by adding to your .htaccess the following lines of code:
RewriteEngine On
RewriteCond %{HTTPS} off
RewriteRule ^(.*)$ https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
And you are done 🙂