Clear cache on multisite subsite mapped to different domain?

I'm running a multisite with subdirectories. Hummingbird is network activated. A few of these websites are mapped to different domains. When updating a post on a site that is also mapped to a different domain, the content is not being updated/page cache is not purged.

How can I get the cache of posts on mapped domains to be cleared when post/page is updated?

Thanks!