most of the times altcoins move on their own and based on their own pump and dump cycle. so if bitcoin goes up or down there won't be any real effect on them anyways.

now there are some coins that pump just because bitcoin is going down as we saw a couple of weeks ago with Dash and Ethereum. these will always get dumped very hard when bitcoin price goes up because their lies become clear.

but the reverse is not always true though. meaning when bitcoin goes down there is no guarantee that these altcoins go up because it can very well be in their dump period.