the way it works is,
1. Time moves slower on different size maps (but not on maps that are small or medium and are expanded to a bigger size.)
This is so that it doesn't take hours in game time to walk across a big prison, but keeps small maps running nice and fast.
in your save game, you can see this up top: "TimeWarpFactor 0.5000000" (that's half speed, for large maps.)
2. For some reason, introversion never adjusted the need timers to match the in game speed. So on a large map, while 3 in game hours have passed, the prisoners are acting as their needs haven't been met for 6 hours. This is why on large maps your cons wake up furious they haven't urinated or showered, even though they were fine before they went to sleep. One of the most annoying aspects of the game, it really kills immersion to have riots every other day because prisoners can't wake up at night and walk 2 feet to the toilet in their cell.
3. There's a great mod by murgh, which basically doubles the timers on all needs. The only catch is needs get written to the prisoners once they check in, so you have to either start with the mod enabled, or use a mod to delete all your prisoners.
As of this update, the mod no longer works properly. You may have noticed other need issues like not getting books from the library to fulfill literacy. The ideal is that Paradox just fixes the whole timing/need thing once and for all, including scaling both up whenever you expand your territory.
