Yesterday I hit gold with turking and decided to transfer my money over to my bank account. I did the instant verification thing instead of waiting 4-5 days. Amazon Payments says my transaction was completed but I'm not seeing any money in my bank account. I made the request after 6 or 7 PM PST.
Usually takes about 24-48 hours to show up in my bank account. The instant verification just verifies that the bank account is legit and that it's yours. The actual transaction works more like a direct deposit or PayPal transfer. MTurk has completed their end of the transfer; it's just sort of in the ether until your bank accepts and posts it.
Most banks make funds available the next business day after the deposit is made. Since it was deposited after the close of business yesterday it counts as being deposited today and will (hopefully) be available tomorrow. You mentioned in the other thread that you're with BoA so this might help too: http://factsaboutfees.bankofamerica.com/understand-bank-practices/deposits-and-holds/