Funnel tracking seems to have a problem with a funnel configuration which is running over two domains.

Background:
I'm running a website with two domains (www.xyz.com and service.xyz.com). Both domains are covered with my tracking script and both domains are configured as "URLs" for aliases:
_paq.push(["setCookieDomain", ".xyz.com"]);
_paq.push(["setDomains", [".xyz.com"]]);

Now I configured a goal with a funnel:

• The first funnel step is reached at www.xyz.com/abc.
• The second funnel step is reached at service.xyz.com/secondpath
• The goal is reached at service.xyz.com/successpath

If I set the funnel in the second step with "Path contains" and value "secondpath" then the url service.xyz.com/secondpath will always be wrong listed as exit url in step 1.
If I set instead the funnel in the second step with "URL starts" oder "URL matches expression" to "service.xyz.com/secondpath" then step 2 is correctly reached in the funnel.

Same problem happens with the goal, when i configured without hostname. The goal is reached in "Goal-statistics", but not reached as goal in the funnel. The Goal-URL is listed as exit url in the funnel.

Do I need to configure the full path in funnels?