The Tiled Background doesn't support animation, neither Tilemap.
But I just saw this tutorial : https://www.scirra.com/tutorials/1352/animated-tilemap
And this topic where some workarounds are detailed : animated-tiles-using-s-p-a-w-n-s-p-r-i-t-e-s-functions_t174105
Alternatively you can spawn sprites of animated water at visible water location on top of your Tiled Background, like every x seconds, that are destroyed at animation end. Or you can apply WebGL effect like "Water" or a kind of distorsion on your fixed Tiled Background.