Apple Pay opening when you tap your phone on a Kisi Reader is a known issue that Apple is yet to resolve. The Kisi Reader has an NFC antenna to read Android devices and when an iPhone approaches any NFC device, Apple Pay opens.
A possible workaround would be to either turn off Apple Pay on your iPhone or open the Kisi app and swipe the lock. The tap to unlock feature may not work reliably for those users with Apple Pay enabled.
Kisi does not collect any sort of payment information (or card details).