Is value of altcoins tied to bitcoin?

Ok, probably the stupidest newbie question ever, but here goes.....
It probably shows I have no idea how currency markets work and should learn some stuff, however I would apprecaite a kind soul to take pity and explain price movements to me (examples would also be nice)

I was buying some altcoin on Bittrex and saw that I could only buy with BTC, which led me to think...
(all numbers below are made up, partly for the ease of the maths)

I buy 300 XVG for 0.001 BTC on Bittrex, BTC value at the time makes 0.001 BTC = USD$20
Now the price of BTC/USD falls and say 0.001 BTC is now worth USD$10
Does the XVG/BTC value change to reflect this, ie 300 XVG is now worth 0.002 BTC?
and vice versa
Or does the XVG/BTC stay the same, in which case to convert my XVG back to USD via BTC would mean that the value of XVG has now also halved?
In which case I may as well never have converted XVG.....

I'm guessing there is probably a lag, as BTC alters, the ask and bids of XVG alter too.
I'm also guessing that with the trading of XVG the relative value against BTC also changes, even if BTC/USD does not.

So going back to Bittrex, BTC is aways shown as having 0.0 change and all other coins rise or fall relative to their BTC value.
And going back to XVG, how do I calculate the value in USD (or any other fist currency) at any one time, is it by converting
XVG to BTC to USD..... and now I'm back in my thought circle, the value of my XVG is totally dependant on the value of BTC to USD even if the XVG/BTC rate never changes.

Aaaarrrrggggh

Thanks in advance.