Welcome to the forums.
Normally Zimbra will only use one server for authentication unless you have the following set:
That will allow you to migrate users to your external LDAP as you need. Do note that currently there is no synchronisation between external and internal authentication mechanisms (there is an RFE in bugzilla for it for passwords. It will also mean that if your external LDAP is unavailable your users will still be able to login to their email.
su - zimbra
zmprov md domain.com zimbraAuthFallbackToLocal TRUE