The Ordered Date Time and its Time zone which is available to fill in Purchase Order Migration Template is for the 'Ordered Date Time' at PO Header level., But it's not available in the PO.
And the Order on date field appearing under Item tab->Basic details of PO Edit screen is not available in Migration template.
SAP Business ByDesign
This field though stored in backend, is NOT exposed on the UI currently- General Tab of the PO Edit screen. So you can make it visible in the Output forms through adobe lifecycle designer mapping of fields.
However ,the Item's Ordered On date is the date when migration has happened and not related to the 'Order Date' in Migration Template's General Tab.
If you think you will require this field to be available in the PO general Tab or you want the item level field to appear in migration template you may Submit your requirement in Customer Influence Forum:
Order date, Order on date , KBA , AP-POP-PO , Purchase Order , Problem