Actually, I think it's a bug with the updating your own money.
I had 78 Gil (I thought it was 76 though), and I deposited 76. On the next screen it said I had 78 Gil still, and 76 in the bank. I deposited the last 2 Gil, and on the next screen it said I had 2 Gil and 78 in the bank. Then I just refreshed the page and it said I had 0 Gil on me and 78 in the bank. Notice anything?
It seems to me that the screen shown after depositing/withdrawing has the up to date value on your deposited money, but the old value of the Gil you're carrying (until you refresh it or load the bank page again).