I have recently set up a bank feed to ANZ and am having a similar issue, transactions received with a date one day earlier than what is listed in the bank account. It also does not bring in the transactions until a couple of days after the transaction date as shown in the bank account.
Having used Xero in another company, these transactions would have appeared early the day after appearing in the bank account
Is there any way to see what transactions are in basiq? Could this be a time zone issue given I am in AWST and the bank is in AEST.