Should I expect to see an amended return in TurboTax with an updated refund amount for unemployment tax?

I heard that the next round of unemployment tax refunds was sent this week, but haven't received mine yet. Will my actual return be updated and should I see a new refund amount in Turbo Tax? Neither of these has occurred so far. We definitely paid tax on my husband's unemployment as we filed in February and (I believe) meet all the other criteria.