The problem you're having is common when configuring multisite domain mapping with SSL. When wildcard SSL is enabled on the main site and the WP Admin is forced to SSL, the mapped domains do not have SSL, and links to the frontend in the WP Admin show as HTTPS even when the home URL is defined without SSL. This problem can be seen when using the WordPress MU Domain Mapping plugin in conjunction with Mercator.
One possible solution is to use a plugin that addresses the issue of SSL with mapped domains specifically. There are several plugins available to assist with this, including WordPress HTTPS (SSL) and Really Simple SSL.
Another option is to configure the SSL certificate for the mapped domains manually. This can be accomplished by purchasing and configuring an SSL certificate for each domain.
Finally, there are several solutions to the SSL with mapped domains issue in a multisite setup, including using a plugin or manually configuring the SSL certificate for each domain.
Here are two examples of how to configure SSL for mapped domains in a multisite setup:
Using a plugin: One popular plugin for configuring SSL for mapped domains is WordPress HTTPS (SSL). This plugin automatically detects and configures SSL for your website, including mapped domains. To use this plugin, simply install and activate it, then go to the plugin settings and enable SSL for the entire website or specific pages.
Manually configuring SSL: Another option is to manually configure an SSL certificate for each mapped domain. This involves purchasing an SSL certificate for each domain and then configuring it on your web server. The exact steps for configuring the SSL certificate will depend on the web server software you are using, but the process typically involves generating a certificate signing request (CSR), purchasing the SSL certificate, and then installing the certificate on your server. You will also need to configure your server to redirect all HTTP traffic to HTTPS.