Depending on the version, Entourage uses one of two proprietary Microsoft protocols to talk to Exchange. Zimbra doesn't speak either of these, and never did, although there is an RFE that you may want to vote for:
Bug 38631 - Enable snow leopard messaging features, Outlook for Mac 2010. (Outlook for Mac 2010 will use Exchange Web Services, which is also used by Entourage for EWS and is an option for Snow Leopard.)
Instead, at one time, Zimbra used iSync to allow Entourage to sync with the server. This is only supported on Mac OS versions prior to the introduction of CalDAV support in iCal. In other words, Mac OS 10.4 and earlier. It also requires you to use the Zimbra iSync connector 5.0.5 or earlier.
Full details are in
this thread and links off of it.
Essentially you might be able to get it to work if you can get your hands on the 5.0.5 connector. But you might also need to be running OS 10.4. It also might only work with Entourage 2004, not 2008. Read the thread thoroughly; if you follow the links, there are instructions for obtaining the old connector. However you'd be using an unsupported configuration.
Alternatively--and this is a long shot--you could try using CalDAV to sync iCal, and then use iSync to sync Entourage with iCal.
What I really think you should do is: open a support ticket with Zimbra for the invite timing issue with Outlook.