How can one force Apple Photos to update the Persons album and to synchronise the Persons album between iPad

The different system versions might be the problem, because the face detection algorithm has changed again between iOS12 and iOS 13. I had go confirm the detected faces again and add them to the People album when I upgraded my Mac to Catalina and the iPad and iPhone to iOS 13/iPadOS 13.

It is not that easy. The upgrade has changed the algorithm for the face detection and the face recognition. The set of faces detected on iOS 13 is slightly different from the faces detected on iOS 12. The position of the detected face may differ slightly and additional faces may be detected. Sometimes it is just not obvious, if the previously assigned name should be transferred to the faces detected by iOS 13 or not.

For example, I had a few photos of two people together, let's say Mickey and Minnie. On iOS 12 the face of Minnie has been detected by Photos and named Minnie, but Mickey's face has not been recognised in this photo. On iOS 13 the opposite happened: Mickey's face has been detected by Photos, but Minnies's face has not been recognised in this photo. Photos has only one name for this photo - Minnie and one detected face - the face of Mickey. If it automatically assigned the name Minnie to the only detected face in this photo, the People albums of Minnie and Mickey might get merged. I prefer it, that Photos seems to be cautious and rather asks for confirmation, than risking to merge people accidentally, because that would really be a lot of extra work to fix again.

Which system version is running on your iPad and iPhone?

You need at least iOS 11 on both devices. Earlier versions of iOS cannot sync the faces with iCloud.