Why does my NY State return start with the Federally Adjusted Gross Income total even though a third of that income was from a previous job outside of NY?

For New York Non-Resident returns, the summary page can be misleading, because it appears that your entire income is taxed. But, what is happening is that the amount labeled as Amount Taxed By New York is actually just being used to find the Starting Amount (your New York State Tax). 

Then, the Starting Amount is multiplied by your Income Factor, which should be the amount you earned in New York divided by your Federal Adjusted Gross Income. 

The resulting tax due is the amount of tax that you would normally pay in your tax bracket for all of your income, reduced so that you only have to pay for the percentage of that tax that you actually earned in New York.

As long as the correct amount has been allocated during the state interview portion as being your only source of New York income, you can feel confident that TurboTax is accurately calculating everything for you.

If this does not fully answer your question, kindly post additional details below.