I think it works out like this, they work backwards for back 9, i.e if tiffer birdies first 8 holes, but parred 9, his opponent parred 1st, but birdied all the rest, he would go top. I'm sure its a count back from 9 down
so if scorecard was like this:
tiffer : 1 2 3 4 5 6 7 8 9
par birdie par bde par bde bde bde bde tiffer 30
bde bde bde bde par bde par par bde opponent 30
Tiffer would go top as his countback is a better score than opponent as he birdied the 3 holes from 9 back, his opponent only managed a birdie then 2 pars. so tiffer, maybe the hole you missed your birdie on was 8, your opponent 4, or maybe you both parred 4, your opponent also parred 1, but eagled 5, this would make him top with better countback score.