"Or do they just look next year to make sure he has taken two."

Not next year; this year (2023). In 2022, your taxpayer met the RMD requirement and took it by the due date. In 2023, they take an RMD. From now on, every year, they take an RMD. There is no more waiting to the tax filing due date.

And since he took the 2022 in 2023, only 2023 will have 2.