No. "5 days early" is 90% advertising hype and 10% baloney.
Here's the technical details. When a bank makes an ACH transaction such as a direct deposit, they first send a notice or "advice" to the receiving bank, letting them know the name, account number and amount. That allows the receiving bank to verify the account number is correct and there are no holds or other interferences, and they send confirmation back to the sending bank. Then the sending bank sends the actual electronic money transfer, and the receiving bank sends back confirmation. The process is supposed to take no more than 2 business days to complete, meaning that if the sending bank sends the advice on Monday, the transaction should be settled by Thursday morning.
Now, some banks will not allow their depositor the use of the funds until the day after the transaction settles. And other banks will allow depositors to have their money as soon as the receive the advice. What this means in practice is that if your employer pays on Friday, their bank sends the advice on Wednesday, the transaction settles overnight Thursday to Friday, most depositors would have access to their funds Friday morning, and a few might not have the money until Saturday or Monday. (Those folks may need to switch banks.)
So when Bank X says "you get your money up to 5 days early" that probably means they allow you to access your funds when they get the advice (ie. Wednesday for a Friday payroll) rather than making you wait.
If the IRS says they expect to make a deposit on 9/9, they are probably sending the advice on 9/8. But I don't know for sure. I would not expect you to have the funds any earlier than that.
Also, if you used refund transfer to deduct your fees from your refund, the refund goes to a middleman to deduct the fees, before the rest is sent to your main account, and that will add 1-2 business days (because of the middleman) regardless of the policy of your bank.
