Since most of the major altcoins move up or down at the same time as bitcoin, aren't they all controlled? How does it work?

We can not control bitcoin unless you have more than 50% ownership of the bitcoin. But there is nothing like that. Altcoins are following bitcoins due to money distribution. Because most of the owners of the altcoins are investing in bitcoin. When they get some profits, they will invest in altcoins. So the altcoin prices will increase.