They should allow you to select to receive notifications for any transactions on your account….like alerts.
Some do, but most don't. With all the issues with fraud atm, it would be good to get notified straight away about transactions, so you would know straight away if someone was using your account without your knowledge. I've tried to set it up with as many banks I deal with as I can, but many don't have the option.
Would be good to have stronger authentication to log in if you wanted, like two factor etc. That would also slow down would be thieves. I know that becomes a pain sometimes, but better that than losing all your money.
Then pick a bank that does? Westpac, Macquarie and Ubank are three I bank with who all offer notifications.