I'm going to guess your trainer means keep your butt and hips over the middle of the saddle if you are conscientiously sticking your butt out you will stay in the middle of the saddle.
As for not falling on the horses neck, you should be pressing into the mane with your knuckles, and kind of push back when you are landing. A strong leg and having your "butt out" will help not falling on the horses neck.
From what you are describing, you see like you might just leaning down over the jump, and not following the horses movement.
Pictures are really helpful, try taking some pictures when you are jumping and look at your position, then you can see what your trainer sees.