The park is closed to off-site guests when EMH start. Therefore, they should be shown the way out. It's the price you pay for staying off-site.
Edit: You said it yourself that EMH is partially for on-site guests to get on rides without the whole world being there. Well, if the whole world IS still there, it makes it hard to get around

. And no sprinkles for you, sprinkles are for winners!
That's what we do. I go see all the merchandise, maybe hop on the monorail and ride around, just get settled in.