WooODT Extended uses hooks provided by WooCommerce, so as long as the default WooCommerce hooks are present in your theme or they are not removed/altered on your checkout page, it will work as it do.

If your theme or some other active plugin manipulate default WC hooks then you need to hook the plugin’s functions to the new place/hook provided by your theme/plugin after altering default WC hooks.

To confirm check WooODT Extended on a default theme and/or with no other similar plugin activated. Better to start by deactivating similar plugins one by one and you will get the reason.

If you have another similar plugin and wish to have both the plugin activated, then you need to alter hooks and/or hooking positions, if it is a difficulty for you, simply send a mail to support team, we will take care of it if its doable.