You need to have a Finnish personal identity code and a tax number to be able to order Valtti cards. Both are issued by the Finnish Tax Administration. The Tax Administration will issue Finnish personal identity codes to foreign citizens who arrive in Finland for temporary work.
Start with instructing your employees to visit the Finnish Tax Administration to acquire a Finnish identity code and an employee tax number.
Make sure that the employees' tax numbers are added to the Public Register of Tax numbers. Normally it’s done automatically by the tax authorities when you apply for the number, but make sure they add them to the register. The Valtti-cards cannot be ordered unless the employees' tax numbers are to be found in this register: https://www.vero.fi/en/individuals/tax-cards-and-tax-returns/arriving_in_finland/work_in_finland/