I wish to print when an order is placed, not when it is paid (or vice-versa)

This can be controlled in the plugin settings:

Settings for when to print

N.B. In  WordPress/WooCommerce developer terms, this means “when the woocommerce_checkout_order_processed action is called, rather than the woocommerce_payment_complete action.”.

Posted in: WooCommerce Automatic Order Printing (PrintNode)