It could be that your employee doesn't meet the taxable wage base or was set to Do Not Withhold for federal and state income taxes in the employee setup. That is why taxes are not calculated when processing payroll.
To check if an employee was set to Do Not Withhold, you can follow these steps:
Go to the Payroll menu.
Within the Employees tab, select the name of the employee.
Select the edit (pencil) icon beside Pay.
Next to the withholding section, select the edit (pencil) icon.
Check the Federal Filing Status/State Filing Status.
Also, QuickBooks Online calculates your federal and state income taxes by following the IRS Publication (Circular E), Employer’s Tax Guide. The online system computes the federal withholding based on these factors:
If you need extra help with QuickBooks Payroll, just let me know by commenting below. I'd be glad to assist you. Take care and have a good one, julio-jpacsllc-c.