The IRS post-dates letters to account for mail delays. They know you won't receive the letter on the day they send it, so they add several days to the date of the notice to account for the delay in delivery.
One very good reason for this is a legal one - many notices give you a specified amount of time to respond. By post-dating their notices, the IRS "clock" doesn't start until you actually get the letter (usually before the date on the notice).
Many people get notices like the one you described.
During processing, the government reviews your refund. During the review process, they look for math errors on your return (extremely rare in TurboTax) and they also check if you owe back taxes, unpaid child support, or other debts.
If they need to make any corrections, they may offset (reduce) your refund. In some cases, the correction might even increase your refund.
Once that part's done, the government approves your refund, which means it's ready to be deposited or sent. At that point the IRS site will update with a direct deposit date.