When the price of Bitcoin rises, most of the alt coin markets plummet.
This is a common idea in the market. I do no know how far it is true or is it just a fake conspiracy theory. For me I believe in bitcoin and some altcoins not all. So that does not mean that bitcoin rise will make altcoins fall - if you think that people sell altcoins to buy bitcoin - it seems bullshit to me. But thats just my opinion.
(1) Does that mean that alt coin holders are losing money, or are the lower alt coin prices a mere adjustment in relation to the new price of Bitcoin?
Numerically yes the altcoin prices being lowered, if they sell at that price they will lose money considering they bought the altcoin at a higher price than that. But simple holding the coin does not mean you are losing anything. Its just like holding a penny in your pocket which has lost its monetary value.
(2) How do you determine if you are in the green or red? Do you look at the $ value of your alt coin, OR what it's worth in BTC?
Both are useful to determine that. On the major exchanges, you can listings in USD and BTC and also ETH. But for the sake of crypto we are mainly associated with BTC and ETH price.
However a coin being red or green is not something to be worried about. It is the future of the coin that need to be thought before you invest anything in it.