​They thought they were the kind of highly skilled engineers ​who could help fulfill President Trump’s goal of reviving American​ manufacturing.

Park Sun-kyu said he had ​built factories that make electric car batteries in Indonesia, Michigan and Ohio. Kim Min-su said he had built or worked in such facilities in Poland, Ohio and Tennessee. Nate Cho, an HVAC guru, said he had helped put up a nuclear power plant in the United Arab Emirates and a Samsung semiconductor factory in Texas.

All three are South Korean citizens, and all of them had gone back to the United States this year. Along with hundreds of their compatriots, they were working at a sprawling 2,900-acre complex built by the South Korean company Hyundai in southeastern Georgia to make electric cars. They were finishing up a battery factory at the site, which the state’s governor has praised for bringing thousands of new jobs for Georgians.

On the morning of Sept. 4, Mr. Park said he was in an office teaching a colleague how to troubleshoot a computerized manufacturing system when a U.S. agent carrying a handgun barged in and shouted: “Everyone outside!”

Mr. Kim said he was supervising in a “dry room,” where the temperature and moisture were kept at precise levels for machines to produce sample batteries. A commotion broke out in the room as a security manager called to report a raid by armed officers. Outside, the agents moved swiftly, spreading out through the premises.