No, seeing the message does not mean your refund has been processed and released by the IRS.
When your file your tax return successfully and you choose to pay your fees from your Federal refund, the TurboTax program considers the fee paid, even though the federal refund has not been released yet. This is why you see "Payment Completed."
Where’s My Refund? has the most up to date information available about your refund. The tool is updated daily (usually overnight) so you will just usually need to check once a day. For more on the timing of your refund please see this TurboTax FAQ.
Once you have confirmed that your refund has been released by the IRS and you have selected a Refund Transfer from Santa Barbara TPG (who will issue your refund) you may check the status of your Refund Transfer by visiting their website.
Check the status of your Refund Transfer
For more information, please see the link below:
TPG Santa Barbara Tax Product Group