No one can know exactly when your funds will be deposited. There are
too many variables including differences in bank processing times once
the IRS sends the funds.
The IRS says 9 out of 10 filers who efile and choose direct deposit will get their refunds within 21 days. You can monitor it with the IRS tool mentioned below. Some returns take longer for additional processing due to specific items in the return. Some are pulled at random for more thorough investigation.
NOTE: If you chose to pay any TurboTax fees out of your Federal refund, that is another link in the chain, since your funds go first from the IRS to an intermediary bank where the fees are subtracted. Then that intermediary bank sends the rest of the funds to your bank in a second direct deposit.
If you efiled, you can doublecheck the status with this tool to be sure it was accepted:
To track a state refund: