The address you report to your employer should be the address where you want to get tax-related mail.
However, you will need to have California state income tax withheld.
Assuming you are on an F-visa less than 5 years, you are considered a non-resident alien. You will be required to file form 1040-NR to report and pay federal income tax on US-source income, but not income you might have overseas. (By the way, Turbotax does not include form 1040-NR so you will need to use different software.)
As a non-resident of California, you must file a CA non-resident tax return to report and pay state income tax on CA-source income, but not income from other states or countries.
Because you are also technically a non-resident of NC (because you are a non-resident of the US for tax purposes), you will be required to file an NC non-resident return to report and pay state income tax on any NC-source income you might have but you won't include your CA income or overseas income.
Income is CA or NC source if you are living in that state or physically working in that state when you get paid. If you did work for the CA company while living in NC, it would be NC-source income because it's based on where you were living when you did the work and not where the payer was located. Other income, like state lottery winnings, would be sourced to the state where you bought the ticket. And so on.
