That is generally correct, although $0.83 Cayman (actually 0.80) has the same buying power on the island as $US 1.00. They are essentially equivalent (the Cayman dollar is fixed to the US dollar at $US 1.00 = CI 1.25, and conversely CI 1.00 = $US 0.80). So if you normally tip $US 10.00 per tank, then you can tip $CI 8.00 per tank and it will be exactly the same value. So, I usually tip CI 16.00 (or 15.00 if I don't have any 1s) for a 2-tank dive, as that is equal to $US 20.00. And if you have only US currency, then just give them US$ 20.00, as many people do. And if you feel like tipping CI 20.00, then realize that that is the same as tipping $US 25.00 (which they may well deserve).
And remember, things on the island are not more expensive because of the exchange rate, they are more expensive because it costs a lot to ship everything in, plus the government imposes a duty on everything that is imported (which is just about everything on the island except the local fish), plus there is a fair amount of wealth on the island and companies can therefore get away with higher pricing. The reason a beer costs CI 8.00 (or $US 10.00) on Grand Cayman is because it's just an expensive place to live, just like a beer costs the same $10.00 (8.00 CI) in New York City because it, too, is an expensive place to live. When exchange rates are fixed (which is not true for most countries), then the value of the currencies are essentially equivalent. When they float (like the US vs Canada) then often one currency is valued more than the other and things do get more expensive for the weaker currency country, but usually these days the dollar is the strong currency, so things are actually cheaper for us when we travel anywhere other than places like Grand Cayman.
Sorry for the pedantic digression. I unfortunately did graduate work in applied economics, and just had to put in my 1.6 cents Cayman.