The zone transfer is not done immiatly (at least for existin one).
For test if is working you should use the test botton in the multiserver page and/or add a domain in your domain list for see if dns go in server you configured aswell
I ran echo "action=rewrite&value=named" >> /usr/local/directadmin/data/task.queue via ssh on the first web box and nothing is showing on the two dns servers, so I think that something is not configured right. I'm presuming zones should transfer in a few minutes ....
try to wait, maybe he didnt started the queue, you shoudl check if in Server /usr/local/directadmin/data/task.queue there is something, if not, the queue has been processed and should be a problem if didnt moved existing domain, if there is something, the queue has not been done yet