OK, an update.
I just went through all the steps described at ZimbraMtaMyNetworks - Zimbra :: Wiki and I found that the zimbra settings do not seem to be the same as the postfix settings:
I have done a postfix reload but that does not change anything. I also tried setting zimbraMtaMyNetworks again through the command line, again no luck.
$ zmprov getServer `zmhostname` | grep zimbraMtaMyNetworks
zimbraMtaMyNetworks: 127.0.0.0/8 10.0.0.0/24 192.168.10.0/24 xxx.xxx.xxx.xxx/32
$ postconf mynetworks
mynetworks = 127.0.0.0/8 10.0.0.0/24 192.168.10.0/24
How do I get "postfix" to see this updated "zimbra" variable?