New York does not tax all of your income. If you have reported the correct allocations, and it sounds like you have, New York will only tax the income you actually earned in New York. However, they do pretend that all of your income is taxable in New York, calculate tax on that amount, and then prorate the amount of tax to the income actually earned in New York.
On the NY return they do make it look like all of your income is getting taxed. But if you see lines 45 and 46, you will see the prorate calculation and the adjustment to NY tax.
Connecticut may well have a similar method for calculating CT tax. However, since you were a part-year CT resident, you will receive a credit for the tax you paid to NY while living in CT.
Your WA income, while factored-in to determine NY (and CT) tax, will not be taxed in either NY or CT.