They don't hide at all...we see them all the time, all over the place in the parks when they are inbetween giving prizes.
When they are actually doing a giveaway, it varies. When I won in One Man's Dream, you couldn't see the DT because they were inside but the regular greeter outside was subtly waving people in. When I won at Soarin' (first ride of the day), I never saw 'em till I got all the way down to the loading area. At Dinosaur, I saw one member when we were in line...he was by the door of the pre-show room. We didn't see the rest till we were in the room, and they slipped through the darkness to the door so they could hand out FPs as we filed out.