It varies, there is usually a relation but sometimes it follow it and other times it goes the opposite and is usually due to the reasons for for the fall in bitcoin.
For example lately alts have gone down worse than bitcoin during falls because the panic from a bitcoin fork has affected the whole market, but in the past during good times it was mostly an inverse relationship where alts would go down when bitcoin was up and vice versa.
Like you said fear of a hard fork which dips bitcoin price so why should alts dip as well when there is no fear of hard forks to the popular altcoins, that means in theory alts should go up correct?
Ok so the past trend of opposites is an old trend that rarely happens anymore?