First, it would help to understand the operation of the mechanism.
The shell, when inserted, is not ever trapped by the edge of the part being called "magazine cutoff". That part is meant to hold the second shell that is in the tube, so only the first shell will follow the bolt back as the shotgun is pumped.
The shell that is inserted into the tube will pop back maybe a half inch to rest against that tip sticking down from the lower side of the bolt face i.e. "the chin".
See that the tip of the shell stop on the bolt is visible in the notch at the front of the carrier. That holds the rim edge of the first shell that is prevented from sliding past that tip due to clearance being restricted by the upper front face of the carrier when the carrier drops back down (the front of the carrier is built at a slant to allow the carrier to be pushed down past a shell at rest there so more shells can be inserted into the tube).
When the gun is pumped, the first shell follows the bolt back while against that tip of the bolt "chin" until the first shell is on the carrier, and during the rearward stroke, the pump arm actuates the shell cutoff to keep a second shell from feeding along with the first.
When the slide is pushed forward and the carrier lifts the first shell so the bolt can push it into the chamber, the second shell will be freed by the cutoff edge only when the slide is nearly fully closed, so that the second shell is now held by the tip on the lower front of the bolt face, just like the first shell.
Lather Rinse Repeat.
Winchester Model-12 Specialist Gunsmith, and others