Tried it just now, what you wanna do is exactly what you were doing, being in the correct isle with the correct box. Once you're in the right spot you want to hover the hand over the box and then left-click to get the items out of the box and drag them onto the self. I'm not sure if you have to hold down the left mouse button and drag or if you can just click once and guide the hand over to the shelf. DON'T RIGHT-CLICK. During my first playthrough of the game, I was right-clicking which caused the box to jiggle out of my hands.
If you want an easier time playing, put all the boxes in the correct isles first. The customers don't spawn in until you start doing your first shelf.