Marking is not only for local manufacturers. If an imported product is in a group that requires marking, the importer must also obtain the codes and make sure they are on the goods.
In practice there are two routes: the codes are sent to the foreign manufacturer, who prints them on the packaging, or the goods are marked after arriving in Uzbekistan, at a dedicated warehouse. The first route needs agreement with the supplier; the second needs label printers, scanners and staff.
Check the current customs clearance and put-into-circulation procedures in official sources and with your customs broker. BDB helps with the equipment and setting up warehouse marking.