I know this question is a bit old, but Minitest is still heavily used, so I hope this could be useful for anyone, as I was slightly confused.
Break down files is in a lot of cases something that you should do. If the new files have the same class name than the others, then we will see the behavior reported by Malik (the files are merged) but also the restriction that @framauro13 talked about. Using this approach, you would only have one setup method available for all the files.
What really makes sense is to have completely isolated test files. So in this case, we have to break the convention of indicating the controller in the class name of the test file and indicate the controller that we want to test. It can be done this way:
class MyCustomName < ActionController::TestCase
tests Some::Namespace::TheController
...
end
class OtherCustomName < ActionController::TestCase
tests Some::Namespace::TheController
...
end
More can be found here in the section "Controller is automatically inferred".