After reading through your post, im still not really sure what it is?
what exactly is tournament mode, and are there any significant things you didnt talk about because they're common knowledge?
Tournament mode is a cvar created for competitive play. However, there are some public servers that run it. On the server that I played on, an admin initiated a vote asking, "Should the next map be played with tournament mode on?" 70% of the people on the server voted "Yes" so the server started tournament mode once the map was started.
Tournament mode has nothing to do with creating brackets and eliminating teams. It simply runs the server with functions that were designed for competitive play.
When the server begins a map and tournament mode is active, players can join the server and run around the map shooting each other, but the game does not start until both teams declare that they are "ready." (This is done by hitting F4. Any player can change their team's status to "ready" or "not ready.") Once both teams are "ready" and have chosen a team name (which appears on the scoreboard), the game begins. In tournament mode, team autobalance is off. In tournament mode, if you are dead, you can only spectate your teammates from first-person perspective, so you can only see what your teammates see, meaning that you can't see behind them and warn them about spies and such.
There are also other changes that tournament mode brings to the table depending on map type:
On arena maps, tournament mode disables all restrictions on how many players can play at once, and teams aren't scrambled. Basically, you get to choose what team you play on and you never have to sit out. However, there is still no respawning in arena mode.
On attack/defend maps (examples being pl_goldrush, pl_badwater, cp_dustbowl, and cp_gravelpit) the game is played stopwatch mode. Team 1 defends while team 2 attacks. Team 2 attacks until they either capture all of the enemy control points or run out of time. Then, the teams swap and team 1 attacks while team 2 defends. Now, team 1 has two ways to win: they can either capture the same number of control points that team 1 captured and do it in a shorter amount of time, or they can simply capture more points.
Example: suppose that team FREEMAN and team COMBINE play a round on gravelpit. Team FREEMAN defends first, and team COMBINE attacks first. Team COMBINE is able to capture control points A and B in exactly 4 minutes and 30 seconds, but team FREEMAN is able to defend C until the timer runs out. Then, the teams are switched and team FREEMAN attacks while team COMBINE defends. Since team COMBINE captured two control points in 4 minutes and 30 seconds, FREEMAN can win by capturing two control points in 4 minutes and 29 seconds or faster. If they manage to do this, then the round ends and team FREEMAN wins without having to attack C. However, if team FREEMAN fails to capture A and B in 4 minutes and 29 seconds, they have a second chance to win: they can capture 3 control points, because team combine only captured 2 control points and 3 is a larger number than 2.
If team FREEMAN captures A, B, and C, and team COMBINE only captured A and B, then team FREEMAN wins because they captured more points. If team COMBINE only captured A and B and did it in 4 minutes and 30 seconds, but team FREEMAN was able to capture A and B only 4 minutes, then team FREEMAN also wins because they captured the same number of points but did faster.
Basically, both teams get a chance to attack, and whichever team captured the most control points wins. If both teams captured the same number of control points, then it comes down to which team took the least amount of time.