The copying of your resource file(s) is done synchronously with the test runner, so I think something else may be going on here.
Check that the tests using the file are not sequence dependent. If there is code specifically clearing out the file, you might find this can affect further test execution. A good way to check for sequence dependent tests is to run them using the Advanced->Run tests using existing process option. Make sure you also check that tests can be themselves run multiple times within the same process - this isn't behaviour that normal test runners do, and sometimes it can cause unexpected results.
