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?

Not Bitcoin, but the crypto market is largely controlled by whales and other industry players. They're the ones who move crypto assets in their favor with their own money. BTC is the #1 crypto in market cap, not because of the whales, but because it has first-mover advantage. After all, BTC is the first crypto that started this craze. Altcoins follow Bitcoin's "footsteps", because every exchange has BTC as the main trading pair. In other words, BTC is the reserve cryptocurrency of the market. Therefore, any price action related to Bitcoin, will quickly reflect on altcoins as well.
It's best to put most of your money into BTC, while leaving the rest on altcoins. That way, you would minimize risks of loss as much as possible. Most altcoins are centralized these days, so who knows if they disappear in the future? Just my opinion
