See
Calendar or Task reminders do not appear in Outlook 2000
The problem is that the default folder is your primary tasks folder, not the delegated one.
With Zimbra, you won't be able to turn this off by changing the "Deliver new e-mail to the following location", since Zimbra does not support that configuration.
There is this product:
Slovak Technical Services Reminder Manager
I have no idea whether this will work for you.
Also, be advised that reminders for tasks do not yet sync down from the Zimbra server.