Your employer's answer obscures the actual process by which you can handle medical expenses paid for with after-tax dollars.
While you are covered by an HSA, if you happen to pay for qualified medical expenses using after-tax dollars (out-of-pocket), you can apply to the HSA plan administrator for a reimbursement of those expenses, even if it is a year or two later (there is no limit in the IRS code when you have to do this)..
Since the dollars in the HSA are pre-tax, you have now effectively paid for those expenses with pre-tax dollars.
What the employer is referring to has nothing to do with "distributions" (when money comes out of the HSA to pay for expenses), but with contributions that you make with after-tax dollars outside of your employer.
Normally, your employer's contributions and your contributions through withholding in a salary reduction arrangement are never reported as income - the amount is removed from boxes 1, 3, and 5 (Wages) on your W-2, but reported in box 12 with a code of "W".
However, you can also make contributions directly to the HSA (such as writing a check) using after-tax dollars, up tp the annual limit. If you do this, you will need to enter this amount separately.
In the HSA interview, you will be asked if you made any contributions (of any kind) to the HSA. Answer "yes".
This will bring up the screen entitled "Let's enter your HSA contributions".
To the right of the second line ("Any contributions you personally made (not through your employer)"), enter the amount of your post-tax contributions.
