If the central, large magnet has its north pole up, then, in order to stick to its rim, the smaller magnets must all have their south poles up. In this orientation, the smaller magnets all repel each other. This causes them to separate from each other by an equal amount.
When you push on one magnet it magnetically repels the magnet you push it toward. The magnetic repulsion travels at the speed of light, and the magnet immediately begins to move. It then pushes its neighbor so that, in a very short time, all the magnets are in motion. However, even though they all start to move immediately, their actual speed is determined by how fast you push the magnet under your finger. That motion is much slower than the speed of light!
This Snack models the current of electrons flowing in a wire: The small magnets represent the electrons, and your finger represents a battery. The magnets repel each other due to their orientation, while the electrons repel each other because they all have a negative electric charge.