Did you destroyed all the cloning orbs in the previous island? The map marks it as red dots.
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Sorry, it was a design error that slipped in due to the constant redesign. The map was wrong and the NPC had no exit. It has been fixed. Now: The map indicates 19 destroyable mission objectives and the NPC must also be escorted to his own exit, there he will give you a key and the exit will be open. Fixed version is uploaded.