Just make sure each time you add a shell to the mag tube that you fully insert it into the tube. Basically you have to sort of go "past" a certain point before you let the shell come back and catch. Just shove your thumb up there real good.
One other note, since you said it is Grandpas model 12, take a look at it and see if it has one or two slide bars going from the foregrip into the receiver. If you see one bar, there is a good chance this gun is also capable of slam firing.
This happens when you pull the trigger, then after the shot you pump the action, and right as you close the action, the gun goes off again on the new round. This happened because you did not take your finger off the trigger after the first shot. So the firing pin slammed in to the primer of the next shell as you slammed the action shut. Technically you can very quickly empty the gun while having only pulled the trigger once. It can be a good thing or a bad thing. Either, way just pay attention to trigger control.