Your own state income tax obligations and your employer's tax withholding are two different things.
Your state tax obligations have nothing to do with what your employer does or does not withhold.
In your example, the wedding musicians would absolutely owe OK income tax on the income they earned in Tulsa - regardless of whether or not their employer withheld OK taxes.
Some states (for example Illinois and Wisconsin) have "reciprocity" agreements, under which a taxpayer who lives in one state and works in another pays income tax only to his/her home state, but OK and TX have no such agreement.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
