They have a test framework that tests your code and measures the time it takes to run those tests. Once you submit your code, TopCoders machines will run a certain number of tests cases against it.
There is no human involved in measuring the performance. They test automatically how much time is spent only in your code.
Usually competitors have local test frameworks that gives them a pretty good idea of the performance of their code. Writing a simple test framework should not be a too difficult task.o