This is not correct: "as long as you will file your taxes separately from your parents, you will be getting the 2 payments,"

When you file your own return, you have to answer the question whether you still qualify as able to be claimed by someone else, even if they are not claiming you.

That's why you use the resources already provided:

If the person is not a dependent in 2020, then they would be entitled to the payment/credit. That doesn't mean "not being claimed." It means "no longer qualifies as a dependent."

You might want to bookmark these links and read the IRS guidance.
Interactive wizards portal for determining dependency:

https://www.irs.gov/help/ita

And:

https://www.irs.gov/newsroom/economic-impact-payment-information-center-topic-a-eip-eligibility

https://www.irs.gov/coronavirus/second-eip-faqs#Eligibility

One for each EIP.

You have to understand Dependency rules.