Welcome Morlock! I hope you're having fun so far.
what are the conditions for them to happen?
You've probably noticed that when you enter the stairs, sometimes you'll get to evolve immediately, and at other times, you don't get to evolve. When you do evolve, you've climbed to the next floor into the next main area. If you don't, welcome to the branch. Although you're entering an area within the same floor and don't get to evolve yet, you may see some cool stuff there.
To see whether you're in the main area or branch, press the backspace button to open up the world map. Branch areas always go sideways from the last room you visited.
Do we have a choice as to when evolutions happen?
You don't get to choose which stairs lead to what place (next floor's main area, yes you'll evolve; if branch, no you won't). When you hover your mouse over the stairs, you may see question marks which means it's unknown to you. However, there are various ways to identify them, and when you do, you'll see the actual location name instead.