The neutrons cause more fission. The process is gentle because only a few neutrons hit anything. Atoms are too far apart. Neutrons are too small. Imagine two magnetic bullets fired toward each other on parallel paths, a half-inch apart.
Bullets move too fast to be drawn into a collision.
They'd have to move slowly to collide. In a nuclear reactor, engineers surround uranium with water. Neutrons enter the water and are slowed down. Those that ricochet back into the core can easily hit uranium atoms. That's when fission takes off.