Yes, you are somewhat correct. Price for bitcoins and altcoins is somewhat co-related. They show is constant growth if any of them starts having the pump or dump. Usually most of the people or traders trade with altcoins keeping bitcoin as their trading pair.

In this situation, they might need to sell their bitcoins in order to purchase other altcoins which might derive the price for bitcoins on a descending graph if the quantity of such traders is maximum in number. This might than go contrary as you said. Each time when the bull runs arrive, bitcoin is the first coin to show us some progress which is then followed by other major coins. Minor altcoin are the last in queue to join the bull runs.