I haven’t read anything to confirm this, so take it with a big grain of salt.
What I know: The amount of first two stimulus payments are ultimately dependent on your 2020 income. Since “they” wanted to get the money to people ASAP, the easiest way to determine how much to send was to use the most recently filed 1040. For some that was 2018, for others that was 2019. On the 2020 FIT forms the payments are reconciled to the 2020 income. If you got too much in stimulus payment, lucky you - no need to repay. If you received less that you were entitled to, the difference is given to you as a refundable credit on the 2020 FIT return.
What I am assuming: The third round of stimulus payments will also be ultimately based on 2020 income. There is the same desire to get checks out quickly, so payments will again be based on the most recently filed 1040. That may be 2019 or 2020. Then the reconciliation will happen when we file in 2021.
The timing of your 2020 return only matters if you had higher income in 2020 than 2019, that higher income is enough to phase out/negate the third stimulus payment, and you are trying to get the payment before the government figures out you aren’t entitled to it.
For everyone else, you will at some point get what you are entitled to — but it might not happen until 2021.