No. California does not use residency dates to compute California tax. It uses the percentage of California income versus total income as if all your income was taxed by CA.
As a nonresident, you will have to make adjustments in the Nonresident Adjustment section of California to tell TurboTax which income is California income.
For the tax computation, CA starts with federal adjusted gross income and then subtracts your federal itemized deductions to come up with California taxable income (after some state-specific adjustments).
This is the base tax, or the amount of tax if all your income was earned in CA. You are then taxed on the CA percentage of this income. So if 10% of your total income is from CA, you pay 10% of the base tax.
You can see the calculation on lines 31-38 of Form 540NR.
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