Whether it's diffeent places or just different rooms/floors of the same hotel (guarded/protected so they can't see/hear each other), they must still have to leave one by one, so there must either be a whole fleet of cars enough for each person to have their own, or the cars must be coming and going all evening for a while if it's, say, 20 or 30 min back to the hotel, and then return for the next people, and then need 5 or 10 min to get the person inside without the next car seeing. And the cars with the traitors circle round and come back to the castle, though I guess they could drop them in some secret place where they have to wait until the other traitors eventually get there.
I guess the easiest is just to have 20 cars available, not the 5 that were shown at first. And given all the production crew and so on there, I suppose that's quite realistic, as it could be any cars not just the fancy black matching ones with special number plates!
I don't know if they actually arrive individually in the mornings as well and then put into a room, and separated into breakfast groups for entering - they make it look like a 'carful' arriving at once, but it probably isn't, because then that carful would know that one of them has been separated out, and you'd not get the same chance of a surprised reaction when they find out who's missing.