I've been trying to set this up as well, and have run into one rather serious issue with this solution. In my case "avlsi.com" is aliased to fulcrummicro.com.
Old configuration: include in /etc/postfix/main.cf
mydestination = fulcrummicro.com, avlsi.com
firstname.lastname@example.org is delivered correctly
email@example.com is rejected as an illegal destination
fulcrummicro.com configured as the primary domain in Zimbra
If I do the suggested configuration of
firstname.lastname@example.org is indeed delivered correctly, but mail addressed to email@example.com is accepted for delivery (and later bounced). This turns us into a giant backscatter source and cripples the server under the extra load of processing invalid recipients.
zmprov cd avlsi.com zimbraDomainType alias zimbraMailCatchAllAddress @avlsi.com zimbraMailCatchAllForwardingAddress @fulcrummicro.com
Looking for an alternate solution within the zimbra configuration...