While BTC has nothing to do anything with any altcoin directly, its reputation alone creates a sentiment in people's minds that those other coins can one day do as good as Bitcoin. It's the sentiment that is attached to the market which makes people comfortable choosing those alts. So any movement that happens in the Bitcoin market will affect people's sentiment and that will lead to positive or negative movements in alts market.

Bitcoin is not affecting the market directly, rather people involved in alt market are. They are making decisions based on the Bitcoin market movement which is affecting the alt market. That's it.