I mean the rules for the accrual basis is the only thing that you would be reading. The date that the transaction is put on the books. So in your case the employer didn't book the HSA until after January first and the 401k on the date that the payroll was issued. Which makes sense. The HSA contributions are probably sent on the first of the month and the 401k is probably distributed with the payroll.
Here are the rules for the accrual basis according to the IRS.
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