I am no expert. But you can imagine water as separate particles which attract each other with a certain amount of energy. When you twist your cup the outer most water molecules are getting accelerated, but the attraction between the molecules is too low to accelerate the other molecules in the inner neighborhood.
On the other hand sand. Sand has a high friction value. The sand in the cup seems to rotate instantly. This is due to the high friction value. The inner neighbors of the sand particles get accelerated almost instantly. Maybe if you would use dry and smooth sand and twist your cup very fast, then the effect could look very similar to your cup-water-twist-experiment.
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