Apple has stopped synchronizing tasks (which they call Reminders) using the standard CalDAV protocol starting with version iOS 13. 
Due to this change the tasks can no longer be synchronized not only with older versions of Apple apps, but also external apps like eM Client.
The sync vis CalDAV still exists and works, and it will sync data between older Apple apps and other apps using CalDAV, and for example between two eM Client apps, but not with the current Apple applications.
You can read about this on this Apple support page.