I know you shouldn’t tell them beforehand, but do you show players the disposition of monsters once a conflict starts? I haven’t been, but now I feel like I should.
We don’t. Not sure why you would show them after the conflict begins if you’re not going to tell them after. With us, the GM just describes what’s happening instead of using numbers. “You take out half of the goblins with that blow,” or “The ogre yells at the goblins and they jump back into the fray.” The same for non-fight conflicts. “You made your point and the first mate steps away from his captain,” or “The captain pulls out his hidden treasure map and brings his first mate back to his side.”
We generally do.
Our GM does but only because he’s a Sith Lord and he likes to taunt us.
Is there reasoning behind not telling the players the enemies’ disposition before the conflict, but then telling them once it begins? Unless you mean telling them before they decide whether or not to have the conflict at all. I don’t feel like the disposition should effect whether or not to have a conflict or what type of coflict that would be. You could reveal the Might of the enemy early and let that influence the players’ decision Otherwise, tell them right after the decision is made or don’t tell them at all.
Showing versus not showing makes an enormous difference to scripting. I feel like if the players don’t get to see the enemies’ disposition, the GM shouldn’t get to see the characters’ disposition. 
But regardless of what feels right, I wouldn’t be surprised if there were large differences between the three options.
WTB Word of Thor PST
Whatever works for your group is fine.
I can’t reveal dispo until the players describe what their characters are doing so I can decide which conflict type they’re engaging in based on their description of their actions. However, once I decide that what the characters are doing sounds like a kill conflict or drive off or whatever, I take the stones for my monsters and arrange them in groups in plain view, identifying which one represents the leader.
YMMV
I tend to follow the same approach to it that Thor does. Last time I tried to hide the dispositions I was given the feedback from my players that they didn’t have a visual sense of the mess that they got themselves into. While I did everything in my power to describe it they wanted a little more. From my side of the screen it does seem like it ratchets up the tension a little bit when the players are stuck between a rock and hard place, staring down a stack of stones compared to their dwindling resources.
I think this thread has made me change my mind.
So far, I’ve been keeping monster disposition behind the screen and only giving it if players have made a roll to identify a creature’s strengths and weaknesses. I think I’ve been missing out.
Some interesting points, especially considering the sources. I’m sure this thread will inspire some discussions at our next session.