Most people believe that the price of altcoins' is determined by the price of bitcoin and that they tend to follow it's market movements.
I partially disagree with this. I have studied prices of coins and tokens on CMC and the fluctuations of each currency seems to be unique and independent of any other digital currency. Some show strong pumps when BTC goes down and some heavy dumps when BTC is rising.
Undoubtedly, there are market forces and factors which affects most currencies, this is not influenced by bitcoins price, it rather controls bitcoins' price as well as others.
So when trading or investing, make sure you treat each currency differently as they have different utilities.
Bitcoin doesn't control markets, but... altcoins price are based on bitcoin, that's why bitcoin doesn't control them but it have some influence in them, let me explain. If one bitcoin cost $10,000 and the alts price are based on btc, then if bitcoin lose a percent of his price (lets suppose it goes down to $9k) all the alts loses his 10%, they will cost the same amount of bitcoin, but since btc goes down, when we make the conversion from the alt price to usd we will see that -10% on the cash price.
This is the best explanation. I think the best term is not control but "affect". Btc may affect the whole market because all cryptos are based on btc price. And in the other hand, fiat like US Dollar also affect the price of btc, in some way, since btc is commonly based on us dollar.