Case of the observer on the Ground:
In this case the observer sees that there is no Centripetal Force acting on the water particles. As you know for a body to move in circular path a Centripital Force is neccessary otherwise the body cannot stay on the circle. Because to change the direction of velocity a Force perpendicular to the velocity is required. Therefore the water particles fly away from the center.
Case of the observer rotating on the drum:
For this observer there is a Pseudo Force acting on the particles, as he is in a non-inertial reference frame. Therefore the particles fly away.