You need a data connection but either cellular data or wifi will work. If wifi is available and you are connected it will be used over cellular data. But if no wifi is available, then your cellular data connection will pull the information from iCloud.
Obviously, that means if you have a wifi-only iPad, then yes, you must have an active wifi connection.
The data does not "flow" form device to device. Each device must connect to the iCloud servers to send and receive information.