Companies from Costco to FedEx have faced lawsuits from customers seeking their share of the refunds. CHARLY TRIBALLEAU / AFP via Getty Images The federal government is set to start distributing tariff refunds soon. Some companies are facing customer lawsuits demanding their share. The lawsuits target companies from Costco to FedEx. Companies are set to start getting refunds on President Donald Trump 's unconstitutional tariffs. Some customers are suing to get a cut of the money. US Customs and Border Protection told shippers last week that it would start issuing refunds as early as Tuesday to companies that have applied. The agency did not comment Monday when asked whether it was on track to issue those payments. The story doesn't end there, though. Customers are suing some companies for a share of the refunds they say they paid through higher prices and fees on goods and services. Nike is the latest target.…