Your stepfather would only have to report the income if he had total taxable income above the standard deduction ($12,200 if single, $24,400 if married filing jointly with his spouse). If he is under the filing threshold, he does not need to file a tax return and you will still qualify for the credit. It is only tax evasion if he is required to file a tax return and does not report the income.
The tax exemption for paying nanny tax to a parent (the parent exemption) is an exemption from withholding and paying Social Security, Medicare, and Unemployment Insurance taxes on the wages. But IRS publications related to Household Employees (Nanny Tax) do not clearly define parent so you have to look to other ares of the tax law to determine if a step-parent qualifies as a parent for this purpose. Publication 501, related to dependents, lists a step-parent as a qualifying relative for claiming them as a dependent so it is likely that a step-parent will qualify as a parent for purposes of the Nanny Tax as well.
But the first thing you need to look at is whether or not your stepdad qualifies as a Household Employee. If not, the exemption from withholding and paying Social Security, Medicare, and Unemployment Insurance taxes on the wages would not matter as there would be no "wages".
To determine if your stepdad is a Household Employee, here is a portion of Publication 926 that would be helpful (see page 3): You have a household employee if you hired someone to do household work and that worker is your employee. The worker is your employee if you can control not only what work is done, but how it is done. If the worker is your employee, it doesn't matter whether the work is full time or part time or that you hired the worker through an agency or from a list provided by an agency or association. It also doesn't matter whether you pay the worker on an hourly, daily, or weekly basis, or by the job.
Example. You pay Betty Shore to babysit your child and do light housework 4 days a week in your home. Betty follows your specific instructions about household and child care duties. You provide the household equipment and supplies that Betty needs to do her work. Betty is your household employee.
It seems it would be relatively easy to not have your stepdad qualify as a Household employee.
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