When disabling SSLv3 in Zimbra, setting zimbraMtaSmtpdTlsProtocols equal to !SSLv2, !SSLv3 is not enough by itself.

Use the following as well:

postconf -e smtpd_tls_protocols='!SSLv2,!SSLv3'

postconf -e smtpd_tls_mandatory_protocols='!SSLv2,!SSLv3'