Your employer is correct. Withholding does not take into account your whole income. It looks at things job-to-job unless you take the extra step to complete the Multiple Jobs Worksheet in the instructions for Form W-4.
If your only income came from a part-time job, it’s possible no tax would be taken out because you would not make enough to file if that was your only income for the year.
For example, the standard deduction for a single filer in 2022 is $12,950, meaning you would owe no tax if your total income was less than that, which works out to $498 bi-weekly. $284.35 is less than that, so no tax would be withheld.
However, when you add your part-time job to the rest of your income, it becomes taxable.
TurboTax has a free W-4 Calculator to help your complete a Form W-4.
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