As per my understanding, I agree with your table except for row 8. By this description
…after round 7 the condition
… is not met, and so I believe that there are two byes in round 8 - one for the first tier winner, and one for a player from the second tier. So the table would continue like this:
5 2 10
6 1 6
7 1 3
8 1 2
9 1 1
… and then the finale takes place in the tenth round.