How do I know if Turbotax has calculated the unemployment exemption? I'm using online software so I can't see actual forms.

I can assure you that TurboTax Online has been updated and is correctly calculating the tax on Unemployment Insurance Benefits in accordance with the American Rescue Plan, which waives federal income taxes on the first $10,200 of unemployment benefits received in 2020 by middle- and lower-income taxpayers.  TurboTax Desktop has not yet been updated. 

If you want to review your return you will need to pay for TurboTax and then you will be able to print your entire return or specific forms/schedules prior to filing.  You will still be able to make changes prior to filing. Follow these steps to print a preliminary copy of our return in TuboTax Online:

• While logged in and working on your return, click on Tax Tools
• From the drop down menu click on Print Center
• Click on Print, save or preview this year's return
• On the next screen click on "Pay Now" 
• You may be prompted to "Go to My Info" if you need to add additional information
• Submit your payment information and you will be able to print your tax returns

Note, you must pay by credit card in order print or preview your preliminary return.  You will not be able to pay using your federal tax return.

Thanks for your response! The reason I am uncertain is that my refund amount has remained the same from when Turbotax had apparently not yet updated and after. I would have thought it would go up a bit, or there might be some words telling be about the exemption. Leaves my uneasy when it's not super clear.

you can see the form that matters  --  Schedule 1 line 8.

Use the " Preview my 1040" command