In Baal/Cerb the one minute cool-down starts when the battle is resolved before the battle scene starts, so unless the battle scene takes over 1 minute there is no disadvantage. I do not know what happens if you are attacked or revenged while moving towards Baal/Cerb.

In the Caribbean the battle scene is a problem because if you steal a map while the boat is docked you can not unboard until after the battle scene is over. I have had the map stolen back from me because I could not umboard.