exchanges don't determine the price, USDT is traded just like any other coin so its actually the traders who determine it's price.
The difference with USDT is its backed by the 'promise' that it can always be redeemed for $1. depending on the confidence level in the promise, the closer the actual price will be to $1.
I suppose in that sense its not really a 'peg'. As you would expect a peg to mean somebody is always actively buying at the pegged value and preventing it going below.
but what is the "promise". Can I sell it back to Tether for a dollar? I assume not. So I don't understand what the point of this "promise" is if it's traded on an exchange like every other coin