How does the gasoline pump know when my tank is full?

If you were to look down inside the tube the fuel comes out of (be careful not to spray yourself with gas) you'll notice a small tube inside the larger tube. That smaller tube detects pressure. Ordinarily, as fuel passes the tube a small vaccuum is created but when the fuel level reaches the top some fuel is pushed into the smaller tube resulting in a positive pressure. This change shuts off the fuel.

A backup occurs in the gas hose and it triggers a valve to shut off the pump. All this happens in about an eighth of a second.

It's magic, no I dont really know that is a good question it must have something to do with pressure or something. I will keep an eye out for a good answer

there's a little man inside and he pushes the button on the pump to let you know when it is full LOL

well no point me answeringthis cause Kelsey B got it right.

flow rate feedback,

some of them do, but you shouldn't count on it. it might be dangerous