I've used this plugin on a few websites and this is the first time I've run into issues. I'm not sure if it is entirely the plugin as I literally just transferred the domain and installed SSL so it may still be setting up.
Anyways, it seems if I have Force SSL Exclusively checked it causes a lot of issues with links. Mainly it's just leaving out the domain altogether. When I click on a menu link like mysite.com/contact then it just goes to contact without a domain or anything. I have it set up on other sites with this option checked and never had this problem.
Turning this off fixes the problem but the entire site is SSL. Not an issue but I'd prefer only the pages I need. I'm going to test later to see if it is the site's DNS or now.