Q: When someone is leaving a region like the city expansion or dungeon or middle ring, can they move normally without stopping at the entrance as if it weren't there?

Yes.

9 minutes ago, Bludgeon said:

Yes.

How do you know?

Each expansion with a new board explains this type of movement.

28 minutes ago, Bludgeon said:

Each expansion with a new board explains this type of movement.

No, it doesn't because I read through the rule books for the expansions and it explicitly state that. So far I found a single line that possibly implies you can, but there's no reason for me to make that assumption given that you have to stop when entering. It says you may move clockwise or counterclockwise after leaving a region if you can do so, but it doesn't say if you have to stop first. Picking the direction to move might only be relevant after you've rolled a die on your next turn in order to clarify that you don't need to conform to the previous region's movement arrows.

You don't have to stop first. Otherwise it would stipulate it in the relevant rulebook!