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If you want to stamp the Timesheet field when it's created, you can make a WF on the Timesheet level. Update your field, and set it equal to $Workitem.ParentProject.myProjectField. This is assuming you're reporting on Milestones and/or Tasks.
If you want the Timesheet field to mimic the Project field, when the Project field is updated. Make a WF on the Project level. Eval criteria isChanged($myProjectField). Update field. Select Aggregated Time Entries Fields. It'll look like $Timesheets.myTimesheetField. Set this field equal to $myProjectField.
Hope that helps.