Sharingan tombe doent introduce new powers, they introduce amplified levels of the power sharingan contains at a GREATLY reduced chakra consumption.
Sasuke could always read movements with Sharingan, but naruto was too fast. Him seeing narutos movements was not the beginning of his precook, it was the evolution of it. He was suddenly able to see movements far fast than he ever could before, to such a degree and such detail and speed, that it almost looks like sasuke knows his opponents next move before they have even decided themselves.
Look back to how Kakashi explains it against Zabuza.
Sasuke could always read movements with Sharingan, but naruto was too fast. Him seeing narutos movements was not the beginning of his precook, it was the evolution of it. He was suddenly able to see movements far fast than he ever could before, to such a degree and such detail and speed, that it almost looks like sasuke knows his opponents next move before they have even decided themselves.
Look back to how Kakashi explains it against Zabuza.