Caching multiple domains (not multisite)

I have two domains pointing to the same WordPress install.

Domain 1, my main domain, displays my full content. Domain 2 will display only content with a specific tag.

It’s all well, but Super Cache seems to get confused about it, and won’t update Domain 2 caching.

I even try to exclude it from caching at all by adding domain2 to SC’s caching exceptions, but it’s not preventing domain2 from being cached either.

Is there a way I can make SC cache those two domains properly or, at least, prevent it from caching one of them?

Thanks guys!

https://wordpress.org/plugins/wp-super-cache/