Thanks for your post. I just found the problem. It is Avast's sandbox feature which I'm running my browsers in!
I tested again, running outside of the sandbox, and now I always get the pop-up notification on both systems when I hit the EICAR signatures.
This behavior sounds like a bug to me, since the A/V engine should still notify regardless of whether a browser is running in or out of a sandbox, especially since it is apparent that it is finding the "malware" as evidenced by resetting the browser connection.