When you configure PSA to use the Show Schedule Grid option, you must ensure that users have read permissions on the schedule object. When you configure PSA to use the Schedule Editable option, you must configure Insert and Delete permissions on the Schedule Exception object.
Timecard pages use With Sharing to retrieve and populate data in the Schedule Grid. With Sharing is Salesforce's sharing rules which are applied and displays records which users have permission to view. You might have to set up sharing rules and configure other record sharing to ensure timecard users can view appropriate schedules. For more information about sharing, search for "Sharing Rules" in the Salesforce Help.