I just realized that I didn't address how tie-breaker games affect advancement or the draft order for the mini-draft.
In previous "thejuice6" tournaments, tie-breaker games have never counted in the calculus for determining draft order for the next round. And that's how I would lean here. Of course, a division winner with a bad record that required a tie-breaker game to win that division just to advance would still get into the next round over the team it just beat (despite the exp win% of each team).
Here is an example of how a 3-way tie would work:
If three teams were tied with a record of 90-62, and two of these teams were tied for first in the NL East and the other team was in second place in the NL West (and also had the worst Exp Win% of the three tied teams), it doesn't make sense to penalize this third team, b/c counting the playoff game would bump the losing team (90-63) ahead of the team not playing a playoff game (90-62).
In other words, the mini-draft draft order is determined after game 162 regardless of what happens in any possible tie-breaking game.
And yes, it would be possible for a team winning a one-game tie-breaker to pick ahead of the team he just beat in the tie-breaker, in the next round's mini-draft.