In the original "Splash" Walter Kornbluth exposed Madison as a mermaid that shocked the world population and scientists wanted to keep her in a lab for scientific study and Alan and Walter took her from the lab to take her to the ocean away from the scientists who tried to get her back. But in this movie Alan and Madison returned to New York and nobody act like they remember Madison being a mermaid and no scientists tried to abduct her.
At the end of the original "Splash", Madison tells Allen that once he jumps in the water with her, he can never go back to his old life, which presumably would include living out of water. But in this movie, not only are they living out of the water on an island, they make a trip to New York.