Found info on the wiki that helped:
ManagingDomains - Zimbra :: Wiki Code:
# zmprov gd example.com | grep zimbraId
zimbraId: ddfa80a1-f22e-47bd-8496-4770d56dd849
# zmprov md alias.com zimbraDomainAliasTargetId ddfa80a1-f22e-47bd-8496-4770d56dd849
This did the trick (no restart of any services needed). Now auto-reply and forward works for both the real domain and the alias domain.