Biometric is not very secure for authentication, but it can be secure enough for identity verification for many applications when there is a trusted witness when the biometric is taken. Biometric is also useful to detect duplicates. For biometric payment, the trusted witness is essentially the merchant. For identity verification, the trusted witness is usually a government employee. Note that four identity verification, the main problem is detecting duplicates and recording biometric effectively prevents the same person being issued multiple identity cards.
Using fingerprint for payment is a calculated business risk vs convenience trade-off. I don't know about the details of the fingerprint banking you're referring to, but I'd guess that merchants that accepts biometric authentication bears the responsibility of ensuring that their customers don't do weird things (like using false fingers) on the payment machine. If the customer or bank claims that a transaction is unauthorized, the merchant would be considered responsible for unauthorized transaction that is issued using their machine and/or merchant account. Many legitimate merchants considers the risk of abusive reversal to be fairly low when considering the transaction limit and additional business they receive due to offering the option. Merchants that facilitates fraud, either intentionally or by negligence, will have to refund any payment, and will be investigated by the bank's fraud team if they detect abnormal pattern of reversals and may become blacklisted.
Risk and security wise, this is not very different than a hand drawn signature, where merchant is supposed to compare the signature visually with the signature on the back of the card. Fraudulent merchant can use a modified machine to record the card number and signature during transaction.
Smartchips used in bank cards and identity cards are essentially very small, low power computer with a secure computation and a storage area that cannot be read out of the card without destroying the chip. The secure storage contains a private key and a card program running in the chip uses public key cryptography to generate a cryptographic signature of the transactions. The cryptographic signature is a very large number regarding a data that cannot be calculated without the knowledge of the private key and would become invalid if any part of the data is changed. In a chip-only transaction (e.g. PayWave, PayPass), the card signs low value transactions without the user needing to authenticate with the card, in a chip-and-pin transaction, the user must input a pin number matching the pin stored in the card before the card signs the transaction.
Because of the much improved security due to the use of cryptographic signature, transactions involving cryptographic chip usually don't put the liability of unauthorized transaction on the merchant. Instead, it becomes the issuer's and customer's responsibility to keep their card safe.
Chip-and-fingerprint can be implemented as a more convenient alternative to chip-and-pin, while being much more secure than chip-less swipe-and-drawn-signature transaction.
In conclusion, yes, fingerprint is not very secure. But when the more secure alternative like chip-and-pin is considered too inconvenient by the target market which readily switch to cash, it is still a security improvement compared to staying with swipe-and-drawn-signature. Note that banks and merchants don't care about the security of your card, if they can offset having to take the burden of the fraud liability with increased transaction volume and faster payment processing.
