Thank you for the NDEF-Hint!
NDEF seems to be a standard-format to store data on NFC-Tags so this is software, not hardware. I downloaded the android "NDEF Writer" and wrote some random value on my cheap Mifea-NFC-card (don't know exactly which). After that, WorkingHours accepts the card.
I guess, the NDEF Writer "formatted" the Mifea-Card before writing that random value - perhaps that's also possible in WorkingHours? (Well, on the other hand, WorkingHours is not a specialized RFID-App...)