It depends if there's a trend for that altcoin. If you check the top crypto you'll see that some altcoins didn't increase much so no matter how much btc price increase if the altcoin's potential is not good then it won't fly high as you said or it's price increasing when btc price increase.
btc is the main coin when btc price increasing then of course it's impact will have an altcoins, but every altcoins did not increased same, like as few altcoins increased in large scale like sonala is increased 10x, and eth, bnb, ton and many others top coins good pumping. altcoins following btc trend, i did not see altcoins highly increased without pumping btc price.