In Bitcoin rally yes they follow Bitcoin price, not all but most of the altcoin increase in Bitcoin rally the same thing happen before breaking ATH of Bitcoin just look at what happen on the top 100 altcoin after that . but in normal price increase they don't the same movement most often . It's only depend on the situation and also depend on what altcoin you own.
Only few alts can follow, most of them are in the top alts. If you can see in the coindesk alone, the charts of alts are following the trend of btc. That is, the top alts only. But most of them, will only follow the trend if they have strong development going on or has active use case. Otherwise, they can't follow the price movement of btc.