This has to do with the way TF2 spawn points work.
It isn't actually truly random - it'll try to spawn you at the first spawn point that was placed in Hammer, but if it's occupied by a teammate, it will instead iterate through the list of available spawn points (in the order you placed them in Hammer) and spawn you at the next free one.
So, in playtests with a full server, you will notice a fairly even split between the three rooms, but that's only if the entire team all dies at the same time.
The first and second rooms will be a lot more populated than the third in practice.
The way you can spawn in different rooms in singleplayer is by doing what The Asylum did and switching classes/loadouts.
For some reason, the game will do the same "iterate through the list" thing it would do if the last spawnpoint you used was taken, so changing classes acts as a way to cycle through all of your spawn points.