If you are looking at the NY % of tax liability, it should match your percentage of days in your case.
If you are looking at the tax, that is calculated differently. New York looks at your total income and determines the tax on all of your income. Then, they take the NY percentage.
For example, the numbers are bizarre and for illustration purposes only:
Earn $2,000 in NY and earn $18,000 in TX
NY says you earned 10% in NY (because 2k/20k is 10%)
NY taxes you 10% of the liability on the full amount of $20k- total earnings.
NY tax on $20k is $800
Your NY tax would be $800 x 10% earned in NY= $80.
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