No. Turbo Tax is never updated when you pay or get a refund from an Amended or Original return. The IRS or state does not tell Turbo Tax anything after they get your return.
In normal times it takes up to 16 weeks or more to process an Amended 1040X return. But these are not normal times.
Sorry the IRS has limited staff due to Covid-19. They just started opening the mail in June that's been stacking up. Back in March the IRS closed their processing centers and stopped processing mailed tax returns. An IRS spokesperson recently said that they have about 11 million pieces of unopened mail. So you have to keep waiting.
See this IRS page for the latest information
https://www.irs.gov/newsroom/irs-operations-during-covid-19-mission-critical-functions-continue
Then once they start opening the mail, After 3 weeks you can track it here,
https://www.irs.gov/filing/individuals/amended-returns-form-1040-x-/wheres-my-amended-return-1