A Touch (Bluetooth) credential will work even if the smartphone or tablet is not connected to the Internet, but a Mobile credential will not.
For Touch credentials (Bluetooth), the smartphone or tablet does not need to be online. The credential is transmitted to the Bluetooth reader (and controller), which then passes the credential to the cloud node, and the Cloud Node stores the Touch credentials and rules and will process them locally.
For Mobile credentials, the smartphone or tablet does need to be connected to the internet to function. If the smartphone or tablet is not online, it is unable to send the credential to the Cloud Node to allow the door to be opened.