When you open the mail tab, the behaviour is as expected: kmail launches as a module inside Kontact. When you open the calendar tab, it opens Korganizer inside the tab AND as an external application. The same for all modules related to Korganizer (but for tasks, for example, it launches only as an external application). SOFTWARE/OS VERSIONS Linux/KDE Plasma: Linux 5.6.3-arch1-1 KDE Plasma Version: 5.13.3 KDE Frameworks Version: Qt Version: 5.14.2
This behaviour has disappeared and I cannot reproduce it: everything is working fine now. I cannot explain what has changed. (Before to fill a bug report, I did reboot and the "bug" was still there.)
Let's close it since it seems to be solved. Feel free to reopen if the bug reappears again.