Cache issue when used with Domain Access

We are using multiple Campaign Monitor (CM) clients, on a multi-domain site managed with Domain Access.
When configuring the module, we are able to add client ID and client API Key per domain, as expected.
However, the available lists (and blocks) are not domain specific. When working on each domain's site, I have to clear the cache or I will see the previous domain's list.
E.g. if I go to domain1.com/admin/config/services/campaignmonitor, clear the cache, and then go to 'lists' tab, I see domain1's campaignmonitor lists. However, if I then go to domain2.com/admin/config/services/campaignmonitor/lists, I still see domain1's lists. I can clear the cache at domain2, and I'll now see the correct lists, but if I go back to domain1.com, I will see domain2.com's lists.

This seems to be a byproduct of the module's cache strategy. Wondering what it would take to make it more DomainAccess-friendly?

Wasn't sure whether to categorize this as a 'bug' or a 'feature request'... it's kind of between the two.