Yes, his income from Postmates is considered "business income" (i.e. self-employment) and is subject to self-employment tax, even if he didn't earn enough to owe any income tax.
He can reduce his self-employment income tax by deducting the costs he incurred to generate that income. The most significant cost would be the mileage he put on his vehicle while making deliveries.
TurboTax Self-employed (or Home & Business) has the interviews and forms needed to identify and report those costs.
