Usually when a Bitzen is in the elevator, it has an exclamation mark notification with a floor they want to be dropped off on. But I have noticed some of them joining with a '?' and then they tell you which floor they want to be dropped off on after you click on the elevator.
Why the question mark notification?
The question mark characters are special characters. Each character "belongs" to a specific floor that matches some part of the story. If the character is delivered to the proper floor, you will unlock a cutscene for that floor.
A prime example is delivering the sticky buns Leia to the interrogation floor.
A question mark is in place of the bubble so that you do not know which floor they are going to, since you could just move their special floor to the floor they are going to unlock the scene. You have to get lucky with the character and floor they are going to.
Any question mark character can be delivered to any imperial floor, regardless of the number floor they are supposed to go to.
Unlocked special characters (Princess Leia, Boba Fett, etc.) are always question marks. From what I can tell, it means they'll never go to a residential floor with an open spot, since they can't move in. There are also regular bitizens with a question mark, but I don't know if the same applies to them.
I've noticed that "?" citizens double the tip when you drop them off at their requested level
For example, a regular citizen shows up to your elevator and requests level 10. You take them to level 10 and then you get a 10 coin tip.
If it was a citizen with a question mark who requested level 10 after the elevator moved, then you will get a 20 coin tip.
If you have any elevator upgrades, the multiplier (x2) of question mark citizens will apply after the elevator's {doubling, tripling, quadrupling, quintupling} is applied.
For example, lets say I have the x3 elevator upgrade. A regular citizen asks to go to level 10. When I drop him off at his requested level he will leave me with a 30 coin tip.
If it is a question mark citizen that requests to go to level 10 after I move the elevator, they will leave me with a 60 coin tip on arrival (10 x3(elevator multiplier) x2(question mark multiplier))
Bear in mind that this breakdown might not be accurate for the holiday-themed upgrade that I just got from Tiny Death Star, because it seems there is now a "figure-out-where-this-character-should-go" type mission for question mark citizens where you are rewarded with cutscenes and other goodies.
Edit: If you want to figure out whether you have the holiday-themed update or not: When you launch the game listen to the music. It will have a "holiday jingle" to it. Also your icon for the game will be covered in snow!
Bitizens with a ? can be delivered to any floor for 1 minute off whatever it's doing, a sales boost, and a double tip .
Additionally, if delivered to a related level, the game will play a scene and add it to your album. See Which characters unlock each scene? for where to deliver them.
I had random bitizens with the '?' Above their head. I found that once you move the elevator they do tell you what level they want to go. But you can send them to any level you want to and they do shave 1 minute off construction time as well as give money. I don't know about the unlocking of the scenes. So far I've only unlocked the initial Mos Espa scene.
Two more things I've noticed:
When you deliver a ? bitizen to a level it frequently causes the same sort of buying frenzy that you achieve with the Celebrity VIP. I don't think it lasts quite as long as the Celebrity VIP's effect.
I've also seen that I get twice the tip for delivering them to their requested level than a regular bitizen pays. I can't confirm that this happens every time, but I've seen it very frequently.
I think there's nothing special to bitizens with a question mark over their head. The only thing it does is make it so you don't know what level they're going to until you start moving them. Normally when bitizens enter the elevator, they tell you what level they want. This can be helpful, for example, if you want to evict a bitizen on a residential level once you know a new bitizen is going to move in, or you want to make sure you're ordering something before a bitizen goes to that level (to reduce the order time). When they have a question mark, you can't know the floor until you start moving the elevator, and you can't stop moving the elevator to do other actions such as evict or order.
Just had one in my elevator and taking it wanted to go to floor -2 which was my second Imperial level. Not only did it give me coins, per usual, it also shaves a minute off any work being done on that level. For example, I was creating Security Codes and had 7 minutes left. After dropping the bitizen off there, a little -1 clock marker hops up on the top right of that level and reduces the time.
Also referenced and somewhat confirmed other people noticing this here: http://quickgamer.net/games/tiny-death-star/walkthrough/
Edit: Just confirmed again sending a ? mark bitizen reduces production on whatever floor it wants to go to by 1 minute.
Edit #2: Also verified that you can send it to any floor to get the time reduced even if it's not the one that it wants to go to. You won't get coins, but it still reduces the time by 1 minute.
Edit #3: Also side note, you can send any bitizen to an imperial floor to reduce the time by 1 minute at any point in the game.
