Yeah, I've found it hard to figure out how and when the second round can take place. I would assume that once you've completed the first round and won, that you can carry on and play the second round. How does it work?
Click game mode, tournaments, bracket, then click on the bracket you want, click full leaderboard, et voila. It opens the bracket and you can see a timer counting down to the end of the round. Once the new round starts, you'll have a play now tab available. You can also do it on this website, just go to tournaments, brackets, then click on your choice and click view bracket and you'll see the same timer.