I was fairly certain this was in the manual and it is. You sorta did it right, it comes back to your city and you put it in any valid space.
Your Tourists must move each round, no matter what.
If there are no valid destinations in the Tourist’s current
Borough, the Tourist must move clockwise or counterclockwise
to a neighboring Borough (remember the limit!);
if this is not possible, the Tourist comes back home to
find a space in your Borough, and is no longer a Tourist.