From my analysis, cryptocurrencies are either in one of three stages; development, introduction or growth (refer to 'Exhibit 1' below). Most coins you see on websites, such as coinmarketcap.com, are in their introduction phase. Coins that are setting up their ICO (initial coin offerings) will be just entering their introduction life cycle. Only bitcoin, I would say, has just made it into it's growth stage given it's mainstream reputation and current adoption by multiple companies around the world (eg. OkCupid, Wikipedia and Steam).
Exhibit 1
(Source: Levitt 1965)
Although a lot of these currencies have been made to solve different problems in the world, they are generally not seen as their own individual currency yet due to the majority being in the introduction stage and this being a completely different market than anyone is used to. This does not mean though, this introduction of multiple currencies for specific purposes may not have been done in the past.
Given they are not seen as their individual currencies, the cryptomarket will generally move with the primary cryptocurrency Bitcoin. Bitcoin, in my opinion, is currently the flag bearer for cryptocurrencies only due to it being the first of it's kind. If bitcoin decreases, most cryptocurrencies tend to decrease in value and vice versa. I would speculate the general exception to this rule would be if something specific happens to a currency, for example if half of all Dash coins are stolen in one day, then Dash's price will plummet due to a loss in confidence of that currency by the market.
Overtime, this will change, and you should see cryptocurrencies make moves up and down on their own with much less correlation with bitcoin and perhaps much less extreme movements (eg. not loosing it's value by 20% in a day). This will occur when a cryptocurrency moves from it's introductory stage to it's growth stage. Allowing for it to define itself and it's purpose in it's own right in the mainstream market.
Sources (Pictures)
Levitt, T 1965, 'Exploit the Product Life Cycle', Harvard Business Review, retrieved 18 July 2017, https://hbr.org/1965/11/exploit-the-product-life-cycle.