Tyreek Hill is sharing more of his side of the recent run-in with police ... claiming things only escalated when cops grew upset with how he operated his window during the traffic stop before the Dolphins' season opener.
Hill's attorney, Julius B. Collins, shared a statement on his behalf ... stating when the NFL superstar was initially pulled over for a traffic violation, he rolled down the window of his McLaren sportscar to hand over his license -- but proceeded to roll it back up.