TMZ Sports spoke to a man who was locked up with 27-year-old Scheffler Friday morning in Louisville ... and he told us the 2x Masters winner couldn't have been cooler during his couple-hours stay in lockup.

In fact, our witness didn't even know Scheffler was a star athlete, at the center of the biggest sports story in the world, until a police officer gave him the 411 ... saying, "You know you're talking to the number one golfer in the world, right?"

We asked Scheffler's fellow inmate about the golfer's demeanor while in custody.

"He kept saying it was bulls*** that he was there."

Scottie was seemingly popular among law enforcement behind bars, too. We're told he was drawing a crowd, with several jail staff and corrections officials popping out to take a peek at Scheffler.

Our witness even says he heard staff wondering how long Scottie would be held before being released.

Turns out his stay was rather fast. Scheffler, arrested during the 6 o'clock hour, somehow made his 10:08 AM tee time ... where the best player in the world proceeded to birdie the first hole (of course), and shoot a 5-under, 66 2nd round at the PGA Championship.

In fact, Scheffler's fast release (8:40 AM) has been the source of some controversy in Lousiville ... with some questioning how he was sprung so fast despite being arrested on 4 charges, including felony assault, for allegedly injuring (wrist and knee) an LMPD detective.

After he was released, Scottie addressed the incident, calling it a "misunderstanding."

"This morning, I was proceeding as directed by police officers. It was a very chaotic situation, understandably so considering the tragic accident that had occurred earlier, and there was a big misunderstanding of what I thought I was being asked to do. I never intended to disregard any of the instructions. I'm hopeful to put this to the side and focus on golf today."