Is Internet connection required to clock in/out?

No, you don't need and internet connection to clock in/out, as long as you do it from the App or Tablet. However, if you want to clock in/out from the web, an internet connection will be required. 

There is an exception in the case of clocking in/out via Tablet or App. The clock/in/out will be stored even without internet connection. The information will updated and display once the device reconnects to the internet. Please note that this does not apply if the clock in/out is via Face ID.