Samsung Pay does not store or share your payment information. For each new transaction, a secure device account number is passed to merchants for payment. Only fingerprints stored on your phone, pin number, or iris scan can authorize a payment.
If you store multiple fingerprints on your device including those of additional persons, those persons will also be able to access your Samsung Pay via fingerprint when fingerprint authentication is enabled. You should only enable fingerprint authentication if you're the only person who has registered fingerprints on your device.