Is there a known conflict between WPMU Domain Mapping plugin and Clear Cache?

I have had some of my subsites (those who installed Domain Mapping) tell me that there new posts were not visible once published. So I tested it myself:

1. I created a new post to test two mapped domains (two of my subdomain subsites) and sure enough, the Cache plugin I am using (Clear Cache) did not "auto-clear" the cache like it's supposed to. Thus, I could not see the new post in the browser.

2. Then I did the same with two of my sites where the Domain Mapping plugin is not yet activated. In these cases, Clear Cache worked as designed and auto-cleared the cache, which reflected in the new posts being visible immediately on the browser.

So, it looks pretty clear to me that Clear Cache and the Domain Mapping plugin do not work together.

Is there anything I can do about this with the Domain Mapping plugin? I didn't see any settings to adjust on the Clear Cache plugin.

If there is not easy fix, I suppose I can switch to a different cache plugin. Do you know which cache plugins work (for sure) with the domain mapping plugin?

Thanks, Joe.