If you made a payment to MN ($250) when you filed your extension, then the program will show that payment as payment with extension, which is correct.
If your return before filing shows 0 in taxes owed, it indicates that your $250 payment was already applied to the MN taxes owed. The $250 would only be refunded if you overpaid your tax liability to MN. Did you expect a refund when you sent in the $ with extension?
From the MN dept of revenue website it explicitly says not to file for an extension:
"You automatically have until October 16 to file before we charge a late filing penalty. Do not request an extension to file."
https://www.revenue.state.mn.us/filing-extensions
There is a place to pay the estimated taxes for MN on their dept of rev website. I did this with the estimated amount I had for MN when I filed for an extension with my federal taxes through turbo tax.
Now I have the same issue as OP where it's still listing that I owe $1500 when I paid $1800. I should be receiving a $300 refund. How should this be handled in turbo tax?
To enter the amount you paid with an extension (including state extension) go to
Federal Taxes (or Personal for desktop H&B version)
Deductions and Credits
Then scroll way down to Estimates and Other Taxes Paid
Other Income Taxes - Click the Start or Update button
Next page second section Payments with Extension
Either Visit All or Click Start or Update by the extension you paid
Pay attention to which year you are entering for a State Extension payment. A prior year state extension payment is also deductible on the federal return so be sure to enter it here.
To get the amount paid on a state extension to show up on the state return……
When you are done updating your federal return, you need to transfer the new federal information by going back through the state tab and the state return. Nothing will change until you transfer the fed info to the state again.