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I was an intern in 2019 between August and November in California on a J1 visa. I filed last year state and federal(1040NR-EZ) tax returns through Sprintax for the year 2019 and received both tax refunds. I was wondering do I need to file tax returns for this year, as in, do I need to report these tax refunds as US income? I talked to some folks at Sprintax and they told me that I don't need to, but I am unsure, because when I checked 1040NR-EZ 2019 form, I have some itemized deductions, which (should) mean that state refund is taxable and I'd need to file tax return(s)?

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If you received a refund of your 2019 CA income tax, that means you overpaid your 2019 CA income tax (probably all of that was paid in 2019, unless you made estimated tax payments or extension payments in 2020). That means when you deducted CA income taxes paid in 2019 as an itemized deduction on your 2019 federal income tax (2019 1040-NR-EZ line 11 or 2019 1040-NR Schedule A line 1a), you may have been allowed to deduct too much, since the deduction is based on actual amount paid in 2019, not your final state tax liability. (I say "may" have been allowed to deduct too much because the state income tax deduction is limited to $10,000 for single or $5,000 for married filing separately, so you may or may not have gotten an extra deduction due to overpaying state taxes in 2019.)

The general rule is whatever amount of "extra" deduction you received due to overpaying 2019 state income taxes as an itemized deduction on your 2019 federal taxes (i.e. the amount your taxable income was reduced compared to if you had paid the exact right amount of state tax), when you receive a refund for 2019 state taxes, you need to put the same amount back into federal income for federal taxes in the year you received the refund.

You would use Publication 525, worksheet 2, to figure out the exact amount you need to put into 2020 income. But roughly speaking, it would be equal to min(CA tax paid in 2019, SALT limit) - min(CA tax paid in 2019 - refund, SALT limit), where SALT limit is $10,000 if you filed as single or $5,000 if you filed as married filing separately. The amount you need to put into 2020 income might be zero or non-zero. If the amount is non-zero, you would need to file a 2020 1040-NR, and report the amount on Schedule 1 line 1.

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