Yes, the IRS will adjust your return if the exclusion amount was not included on your return.
"I paid taxes on my unemployment benefits" is somewhat imprecise. You should get an additional federal income tax refund for the unemployment exclusion if all of the following are true.
If all four of those conditions are true, The IRS will recalculate your tax return and send you the additional refund.
TurboTax Online was updated for the unemployment exclusion on March 21, 2021. If you filed your 2020 tax return with TurboTax Online after that date, the unemployment exclusion was included in your tax return if you were entitled to it. In that case, no adjustment of your tax return is needed.