Hi, I have filed both state tax and federal tax, but paid IRS tax later which not updated in turbo tax tool. How can I get my state refund which I haven't received yet?

The amount of taxes owed shown on the TurboTax Tax home website will not change since TurboTax has no way to know if or when you paid the taxes.

To check the status of an e-filed return, open up your desktop product or log into your TurboTax Online Account. You can find your status within the TurboTax product.

If accepted by the state use this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

Why does my TT account say I still owe tax due?

TT does not update after your return has been accepted.  Your account will always show the result of the return you prepared using the software.  TurboTax never knows if you received your refund —or how, when or even if you paid tax due.  Your proof that you paid your tax will be your own bank/credit card records.

Federal and state refunds come from completely separate entities,  There is no rule as to which one will come first or how much time there will be between their arrivals.

STATE RETURN

Make sure your state return was accepted:  https://turbotax.intuit.com/tax-tools/efile-status-lookup/

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/00/25573