I’m not seeing any cases yet in the Notification plugin code where it would conflict with anything Pods does normally.
Pods does not call an independent wp_insert_post or wp_update_post except in the case when the API is used to save through. So normal post edit screen saves will still happen normally, we do our own saving hook into wp_insert_post to save any custom fields on the page but that shouldn’t be causing the double notification or no notification at all.
The only thing I saw was the draft trigger, where it does not check whether the previous status was previously set to draft already before running, which might cause duplicate draft triggers possibly? https://github.com/BracketSpace/Notification/blob/develop/class/Defaults/Trigger/Post/PostDrafted.php#L58