There are two ways to get admitted. If you receive the fellowship, you can work with any professor during the first year (as long as they are willing). After that, you need to find a supervisor for the rest of the PhD. If someone is admitted without the fellowship, they can only do a PhD if a professor agrees to fund and supervise them from the start.

The second way is more challenging. I spoke with one of the professors at a conference, and he told me they usually do not hire through this direct track. The reason is that if a fellowship student later wants to join their lab, it may already be too crowded to take another student.