What should I do if I submitted taxes using turbotax and I do not qualify for the SPT. My taxes forms are now accepted, how should I correct my tax forms..

According to Department of Revenue of New York, if you are a U.S. nonresident alien for federal income tax purposes and are required to file federal Form 1040NR, U.S. Nonresident Alien Income Tax Return, or federal Form 1040NR-EZ, U.S. Income Tax Return for Certain Nonresident Aliens with No Dependents,  you may be required to file a New York State nonresident return, Form IT203. 

To decide if you need to amend, please review https://www.tax.ny.gov/pdf/current_forms/it/it203i.pdf under U.S. nonresident aliens on page 49 

According to Department of Revenue of Illinois, if you are a nonresident alien, you must file Form IL-1040 if your income is taxed under federal income tax law. You must attach a copy of your federal Form 1040NR, U.S. Nonresident Alien Income Tax Return, or federal Form 1040NR-EZ, U.S. Income Tax Return for Certain Nonresident Aliens With No Dependents.  (If you have already filed the form, you would want to re-submit a Form 1040-NR to IL)

http://www.revenue.state.il.us/Individuals/FilingRequirements/