Card banker checking in. Actually, what FatBaldGuy said is absolutely true: the bank has no control whatsoever over when a check card transaction posts to your account.
Let’s say you swipe your check card for $10 at Wegman’s. The little swipey machine, (called a ZON), sends that data to the bank. If you have the required funds available, the bank sends back an authorization code and places a $10 hold on your account; this is why, if you check your balance immediately after using the card, the transaction seems to have “come out” already [editorial: in truth, I really wish banks didn’t place funds on hold; all it actually serves to do is confuse the hell out of people who think their transactions have already posted]. This leaves Wegman’s with a $10 sales draft, similar to a check, which they must then submit through their merchant bank, who returns it to your bank, who then gives the $10 to the merchant bank and posts the transaction to your account during the next business day’s processing.
Very rarely will you see a check card transaction post to the account on the same day it was made. It can happen, especially if you make the purchase early in the day, and you and the merchant use the same bank – given your statement about when your purchases posted with your old bank, I’d lay odds on which bank most of your area’s merchants use – but it generally doesn’t. More often than not, you’ll see it post during the next business day’s update, which means that, barring weekends, you’ll see it on your account two “real” days after the transaction was made. If a weekend is in the way, that adds two days to the whole shebang. So, here’s my Educated Guess™ as to what happened with the Wegman’s situation.
You swiped your card at Wegman’s on Thursday. Since, as you point out, they probably want their money ASAP, they submitted that day’s sales drafts to their bank for processing that same day. However, they did this after that bank’s cutoff time for same-day processing, which varies from bank to bank, but is generally in the 2:00-4:00 pm range. So, the merchant bank processed your sales draft on Friday night, and sent it on its merry way to your bank. Your bank, like all banks of which I’m aware, does not update anything on weekends, so their next chance to process your sales draft was Monday night. Tuesday, you have a look at your account, and there’s the transaction. To you, five days seems like an outrageously long time to process this very basic transaction, but in reality, there was nothing at all your bank could have done to speed up this process. There are many legitimate reasons to be pissed off at banks, but this isn’t one of them.
All of the above, of course, assumes that by “debit transaction”, you’re referring to a purchase made with a check card using the credit option. If you actually made the purchase as a debit, by entering your PIN, then you’re absolutely right; the absolute latest that should have been processed would have been Friday night. I’ll have to check my Book-O-Regs, but I’m almost positive that delaying it any longer would be illegal if this were the case.