Great question, and you say that the mirror site is still marked as canonical. In fact, you need to solve a couple of problems before they hit your link juice harder.
I suspect the main reason is that MVC, by design, is a URL rewriting system. Thus, depending on the massage that occurs with the originally requested URL, people try to establish a canonical link to the final URL format after rewriting. However, I think you have gained the oversight that most people have - what is “What about the URLs that reached the page that were not expected, and REWRITTEN became the real canonical path to the URL?” The answer here is to rewrite these “bad queries” when you find them. For example: if you rewrote your domain requests with a mirrored ISP domain, then by the time it reaches the loaded page, this is NOW a valid URL; This is because it has been "fixed" according to your rewriting rules. Make sense? Therefore, you will need to update the MVC routes to handle the bad route created by your ISP. NOTE. YOU SHOULD make sure that you are not using the originally requested URL, but the final one, rewritten when creating the canonical link value.
Keep working for my WWW test, not the WWW tip, as well as the fact that you mentioned that you are not processing invalid URLs.
People also do this because your site is already “mirroring” another domain that people always forget about. Subdomain "WWW".
Believe it or not, although discussed, many claim that having www.yourdomain.com/mypage.htm and yourdomain.com/mypage.htm actually harms your page ranking due to "duplicate" content. I suspect that is why people show "the same domain" because it is actually a domain without the "WWW". (I use the rewrite rule to make www vs no-www consistent.)
Also, be careful about “setting up my IIS site to only respond to my site’s domain requests,” because if Google still sees the links there and considers them part of your site, it may actually just punish you for that pages that do not work for loading (for example, 404 s) I recommend having a rewrite rule that sends them to your "real" domain or at least set a canonical link to use only your "real" domain with WWW , or not. (It is argued that this is better, I do not think it matters if you agree.)
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