I think you probably need to get clarification directly from your bank.
BACS payments take three days to clear, but they don't appear on your statement until the third day, so they are usually treated as cleared straight away on the day they show up in your account. However, as they can be recalled at any time up to the close of business on that third day, some banks don't allow you to withdraw the funds until the following day, to be sure that they have indeed cleared and haven't been recalled.
From what the cashier told you, it sounds as though your bank has waited the extra day to be sure the funds are there, but because they said it was due it being the *first* large payment, that could imply that they will look to review this policy later and release the funds to you straight away without you having to wait the extra day.