Im not sure about your statement which says bitcoin goes down then altcoin goes down even more. I have never seen that happening in first place. It has always been the reverse case for altcoins and bitcoin. They never match up because the most popular trading pair is bitcoin/altcoin only and thats why whenever people go for selling the alts then they will do it with bitcoin leading to increased rates of bitcoin and decreased for the altcoins. Thus vice verse case is also true for them.
I have seen it happening many times since the rise of Bitcoin from the first of August this year. Everytime there was a BTC price correction, alts were bleeding even more than BTC. They rise only if BTC stays stable or goes up/down only slightly. If it's more than 3% change of BTC, alts are done for usually. Of course it's hard to generalize this, you would find exceptions to this as well. But I have been following a lot of alts and I would say at least that it happens like this often.
And to add one more layer of complexity: Ethereum-based ERC-20-tokens behave in the same way when ETH rises/falls, not only when it's the case with BTC.