As someone who's help to run several tournaments of varying size let me add my two cents.

For the most part what is said above is accurate. Your teams past performance, league they play in and request from the coach/club is taken into consideration.

Some tournaments will also try to avoid you playing opponents you'd normally see in your regular season. I can tell you as a coach it's frustrating to drive for hours to play someone who is normally only a few miles away.

In the end the tournaments want 1.) For you to come back next year. 2.) For you to have a good experience.

And of course the host club wants to earn revenue as it's likely built into their operations budget if it isn't a brand new tournament.

What order they place those priorities and how they go about achieving that can vary.

Jeff Cup seem to get the brackets wrong every year

Depends on the tournament.

It's a mix of rankings, requests and organizer's knowledge. It a team, by the rankings, is put in group B but there are teams in Group C that beat them handily, then they'll make an adjustment, and stuff like that.

Personally I don't like the way tournaments are run here. I prefer the group stage (shortened) games where you have to play your way into the top groups, especially in tournaments with teams from various areas who don't normally play one another that often.

when you are applying, you can specify which bracket you want to be in, and can provide them recent game results for reference.

When you register a team for a tournament a question about level or division is asked in the registration (usually always). The person registering the team can request placement in a level they feel is appropriate or that the coach/club say they want to be placed in. The tournament director or someone behind the tournament curtain then makes the final decisions but will often take into consideration where the club/coach state they want to play. I've seen two types
The coach club that wants to play their team in the highest bracket possible and the opposite, the coach/club that purposefully opt to play lower level brackets so they get wins and tournament championships.

Politics, $$$, and gotsoccer rankings.

Each tournament has a different system. Many of them do consult with the coaches for each given age group who may know the teams. Some base it solely on rankings. Almost always the goal is to group teams at the same level together although there are a handful of clubs who will deliberately try to stack brackets so their own teams have a better chance to win. Many clubs will also listen to appeals and move teams if they are incorrectly placed. Usually it is the tournament director who has the final say. From what I've heard many tournament directors feel the job has gotten more difficult recently with more and more closed leagues claiming to be elite and fewer teams playing in competitive leagues with promotion and relegation where you can look at their record and tell something about their level.

I am wondering how it works. Does a coach just say, I'd like X team to be in Y flight? Or is there more to it?