Player matching in the second leg (single elimination)

[sillynamenace]

I want to understand how the matching algorithm used in the second leg of a tournament works. I have a specific case in mind.

There's a 15p tournament.
First leg: Swiss, 3 players per game, 5 rounds. After 5 rounds, the first 5 players qualify to the second leg.
Second leg: Single elimination, 3 players per game, 1 player qualifies to the next match.

Now, after the first leg we've got Player1, P2, P3, P4, P5 ranked. (The rest of the 15 players are eliminated.) I'd love to see that in the second leg, P1 and P2 are automatically skipped and that it is P3, P4, and P5 who'll play the first single elimination game. It'd be fair to give this privilege to the 2 best players of the first leg, right? Hence in the second (and last) game of the single elimination leg, it'll be P1, P2 and the best among P3-P4-P5 who'll play the ultimate Final Game of the tournament.

This makes a lot of sense to me. And perhaps this is how it works here. Is it?

The real question, in short: How are the players are matched in the second leg of a tournament of this sort? Is it just random? I hope not.

EDIT:

Actually, maybe my answer is given here: https://boardgamearena.com/forum/viewtopic.php?t=47591

[Meeplelowda]

This is for sure how it works for two-player games. In fact, it's the whole idea behind having a group stage with two groups from which 7 players advance. The winner of each group gets a first-round bye and they are placed in opposite halves of the single-elimination bracket. The other 12 play the first round leaving 6, and now you have a power of two from the second round onward.