It all depends on when they process the refunds for that day. Depending on the timing, they may process it by Feb 4 afternoon, however you bank may not pick it up and clear everything for you until the next 1-2 business days.
I'm not looking for a refund or anything but I do a lot of Accounts Payable and Receivable via wire and ACH and it simply depends on when the bank deems close of business and when the initial payment was processed. That's way I always give about 3-5 days for something to post so nothing is ever late to my vendors.
The only thing that post "same day" immedately is an incoming or outgoing wire which you pay anywhere from $25 to $35 to send and another $12-$15 to receive the funds.
My best suggestion is to call the IRS and get an update.