IT IS NOT COUNTED AS INCOME AT ANY TIME ...
Your 2020 return starts out by assuming you didn't get any Stimulus payment so it gives you the full amount of the credit and that is reflected in the Refund-O-Meter. Then near the end of the interview you enter how much you actually got in advance and the floating refund is adjusted accordingly so you don't get the credit twice.
Check line 30. The Recovery rebate credit is on 1040 line 30. It either adds to your refund or reduced a tax due.
Before filing, You can preview the 1040 or print the whole return
It would be nice if they would have asked for that information in the beginning of the interview like in the MY INFO section BEFORE you entered in the income BUT the programmers did not ASK us posters in this forum AND they probably will not listen to us now and change the interview flow so I have been posting this answer A LOT this year.
They may have been issued using the information from the 2019 return but both stimulus payments were advances of the 2020 credit and must be reconciled on the 2020 return per the IRS rules.