People checking mining profitability before a purchase is exactly how this correlation get established in practice. When they see that mining is profitable, they will buy mining equipment. But profitable is synonymous here with rising prices because the coins which miners receive simply start to cost more. So the higher the profitability the greater number of would-be miners are going to buy ASICs. But as you correctly pointed out yourself, more miners leads to higher difficulty. Thus the correlation between the price and mining difficulty is established.
That isnt anywhere near good enough to be called correlation because we dont know how many miners get shipped and there is a 2 month window before the machines arrive. Furthermore, there will be alottt more machines shipped when there are more manufacturers. Samsung may very well make a loss here but it isnt a big deal to them since they are huge.
For example many new miners ordered units 1-2 months back when profits were farrr higher, around 5-8 times higher and now, when they get their machine, the proditability is a hell lot lower. Thus, there is no real correlation considering how huge the difference is....
A 2 month window explains why difficulty is lagging behind the price. Anyway, you can see on the chart below that difficulty has been following the price pretty close:
Now that Bitcoin has gone down dramatically, we can see that difficulty still rises. This can be because miners are still adding mining rigs as there is definitely some lapse between buying a mining rig and actually receiving it, which you correctly pointed out. If the price doesn't rebound and flatlines from now on or even goes down further, we should see the mining difficulty go down too. If it continues to rise despite Bitcoin going down, then you would be right. So let's wait and see what happens in the next few months.
The mining difficulty will not go down. Why would it go down? People will mine AS LONG AS they can make something out of it....even if it is 50 bucks a month? The only time it will go down is IF it becomes unprofitable to mine. But in that case, that would mean those with lower electeicity cost make like 50 bucks a month and those with higher electeicity cost switch it off.
Both sides lose anyways.
Miners can be mining for a loss for some time hoping that the price will rise in the future, especially if shutting down will cost them some bucks. But if the price markedly goes down as it has already done or even lower to $5,000 and below, mining will likely be no longer profitable for a lot of miners. They will start to leave, and that would mean decline in the hash rate because the rest can't arbitrarily increase their hashes. But if the hash rate goes down for a certain amount of time (about 2 weeks or so), the mining difficulty will get adjusted to match current hash rate. Therefore, if hash rate declines due to miners leaving, difficulty will necessarily go down too. Another question, though, is that they may have pretty high profit margins, so most of them can still remain profitable at present prices and no one is in fact going to shut down, thus the difficulty won't drop.
As an aside, I'm not very familiar with Dash mining, but as far as I know it is a POS coin so we probably can't compare Dash mining with Bitcoin mining, at least not directly. Anyway, there can be a handful of factors affecting mining difficulty where price is just one of them, even though it is a decisive factor which should prevail over other factors in the long run.