POWAY, Calif.—Oscar Stewart was sitting in the back of the Chabad of Poway synagogue when he heard the gunshots, some 20 minutes after 11 a.m. services began on Saturday. He said his first reaction was to run and he sprinted out into the entryway—where he saw the gunman, firing an AR-style rifle down the hallway.

Mr. Stewart, 51 years old, said he shouted and charged at the shooter.

“As...