For anyone who didn't receive a stimulus or only received a partial stimulus (due to not filing previous years, or because their income changed between 2019 and 2020, etc), they can "reconcile" their stimulus when they file 2020 taxes. Any additional stimulus they are owed will be paid to them along with their tax refund.
At the beginning when you listed your income, did you check "received a stimulus"? If you didn't/told turbotax "no", the turbotax system likely assumed you didn't get your stimulus, and as you progressed, it continued to include your owed stimulus in your refund total. But when you got to the end and basically said "actually yes I did get that $1200", the preview number went back to your refund-only total of $5300.
Some explanation/examples: https://abc11.com/tax-return-refund-2021-taxes-stimulus-check/10330411/
Your stimulus was estimated based on 2019 income, but you could get more if your 2020 income was lower. You won't need to "pay back" any of the stimulus even if your income went up. If you need this option, it will show up in your 1040, Line 30 listing the amount of stimulus you were owed but didn't get (and would get along with this refund).
From this turbotax blog post (https://turbotax.intuit.com/tax-tips/tax-relief/2020-stimulus-tax-relief-for-this-years-taxes/L4gtAi...:( "If your income was lower in 2020 than it was on your prior-year return, you could be eligible for a higher stimulus payment once you file your 2020 tax return. However, if your 2020 income was higher than what was used to determine your rebate amount, you won't be forced to pay back the stimulus money or lose any of your refund. Any adjustment to the stimulus payment on your 2020 tax return will be in your favor."
see also:
https://blog.turbotax.intuit.com/tax-planning-2/does-my-stimulus-check-affect-my-taxes-48943/
https://blog.turbotax.intuit.com/tax-deductions-and-credits-2/what-is-a-recovery-rebate-tax-credit-4...
