When you attempt to insert the Last Modified Date and Last Modified By fields while logged in as a user with the Create Audit Fields permission enabled, it may appear that your desired values are not set by the import.
Last Modified fields may not appear to be set with inserted values if there are triggers or automation fired after the creation of records in that object. If that automation performs an update the record, new Last Modified values will be used rather than the provided values. If the audit fields must be populated using the provided values, disable any automation that occurs after record creation..
When the Shared Activities feature Allow Users to Relate Multiple Contacts to Tasks and Events and the Create Audit Fields permission are enabled, the Last Modified Date and the Last Modified By fields will not reflect the inserted value. This is true if the task is associated to a contact or lead (WhoID), or other records such as Account, Opportunity, Campaign, etc. (WhatID) during task insert.
During creation of the associated records, the task is exposed to an update, which results in the Last Modified Date and the Last Modified By fields being updated with the current date/time as well as the user performing the task insert.
Note: The activity setting Allow Users to Relate Multiple Contacts to Tasks and Events is automatically enabled in Professional Edition.
See also:
Enable Shared Activities
Enable the 'Create Audit Fields' permission
Disable a Trigger in a production environment
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