Anticipation.

He or she has been practicing many years, and so it’s second nature, like anything that seems impossible but isn’t.

Training, and good eyesight. Some people process visual stimuli better than others.

Remember, too, that the way the pitcher stands, and placement of fingers on the ball, and even the location of the catcher behind the batter, are all ‘tells’ that suggest the pitch to be thrown. Si that helps in anticipating the pitch.

(Some catchers squat differently when expecting a curve as opposed to a fast ball, for example)

Trash cans also sometimes help.

In case anyone thinks @Darth_Algar is off base, here is a write-up about the Astro’s cheating scandal using a trash can.

While the ball flight time is half a second, the pitcher’s windup and throw takes much longer. I estimate that to be close to a second. I’m sure someone can find better numbers.
All those factors plus experience enable the batter to hit the ball.

Yeah, as @LuckyGuy just wrote, the ball doesn’t just launch from the pitcher instantly. The batter is watching the pitcher and responds to his movement as he throws the ball, before it leaves the pitcher’s hand.

That makes more sense than what the article suggested. It is not that the batter adjusts afterward, but that the batter estimates, before the pitcher releases the ball, when and where it is going to arrive. If the pitcher does a good job of disguising what type of pitch is going to be thrown then the batter may end up swinging too early or too late. It seems extraordinary that a batter can hit a ball that may either be going 100 mph or that may be a curve ball, even with the help of trashcans.