If you are a permanent resident of Oregon and working temporarily in California, then you will pay taxes to both states. However, California allows Oregon residents to claim a credit for taxes paid to Oregon. So, yes you should have taxes withheld for both states in order to ensure that you cover your potential liability.
You should prepare your Oregon state tax return first so that you have the information you need to report on your California state return to calculate your Other State Credit for the amount paid to Oregon that would otherwise be double-taxed. So, even though you paid tax to two states in 2024, you can claim a credit in 2025 on your 2024 California state return to reimburse you for any amount double-taxed.
This is an unusual situation based on agreement between the states. In most cases, taxpayers prepare their nonresident return before their resident return.
Nonresidents of California may claim a credit only for net income taxes imposed by and paid to their states of residence and only if such states do not allow their residents a credit for net income taxes paid to California.
California nonresident individuals, estates, or trusts that are residents of one of the following states or U.S. possessions and paid a net income tax to that state or U.S. possession on income that is also taxed by California may claim the other state tax credit:
Arizona (AZ), Guam (GU), Oregon (OR), and Virginia (VA).
California nonresidents who are residents of any state or U.S. possession not listed may not claim this credit. This credit is not allowed on a California group nonresident tax return.
See this California Franchise Tax Board webpage for more information about the California Other State Tax Credit.
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