It is not clear to me what "credits and incentivized earnings" refers to.
Employers do tie wellness programs with HSAs. An employer can choose to contribute, say, $1,000 to an employee's HSA if they join the wellness program or meet some sort of goal.
In this case, the employee will report the $1,000 contribution, because you have to report all contributions from any source to your HSA. This is true of anything that is actually contributed to your HSA (since all contributions have to be cash).
However, the employer will almost certainly add this $1,000 to the code W amount in box 12 of your W-2, so you will have entered the $1,000 contribution when you enter your W-2. Note that the code W amount is subtracted from Wages in boxes 1, 3, and 5 when the W-2 is printed, so your tax benefit is not a "deduction" but a reduction in your taxable income as described by your W-2.
If by some strange chance, the employer did not add this to your code W amount, then there are two choices - one pre-tax and one after-tax.
Pre-tax
If your employer put money into your HSA, removed it from Wages in boxes 1, 3, and 5, but did NOT add it to the code W amount, then do the following:
1. Navigate through the HSA interview until you see the screen "Did your employer tell you about any other contributions?" Click on "yes". Ignore the reference to "previous year.
2. Three new lines will be exposed. Enter the amount that the employer added to the third line: "Employer and payroll contributions not reported in Box 12 of your W-2".
After-tax
If your employer put money into your HSA, but did NOT remove it from Wages in boxes 1, 3, and 5 (so it is not part of the code W amount, either), then do the following:
1. Navigate through the HSA interview until you see the screen, "Let's enter [name]'s HSA contributions" (see screenshot below).
2. Enter the after-tax employer contribution to your HSA on the second line, where it asks for contributions you "personally" made to the HSA.
