The way it works, as far as I can tell:

You use Duty Finder to be assigned to a group instance.
This instance which is assigned to your group of people from all kinds of servers is not linked to the servers.
You can not trade in here, I assume this is to stop any form of cross server trade. But this also means that you can not have an item drop from the instance transfer over to your original server unless it is acquired while still in the instance.

I know it is sort of silly, but you just have to wait at most for the 200 or so seconds for the timer to run out, assuming not everyone has rolled on it or passed.