I’m guessing you’re using https://packages.debian.org/bullseye/jami? (i.e. Jami version 20210112.2.b757bac) If yes, unfortunately that version is well outdated by now. I’d recommend you instead try installing Jami from our repos on dl.jami.net (for example, for Debian 11: https://jami.net/download-jami-linux/#open-modal-debian-11) so as to get the latest release of Jami. Then if you still experience issues, please let us know here and/or open issues on git.jami.net.
For your question about Jami running in the background, it’s indeed possible: Jami has historically had two binaries: 1. the client (e.g. jami-gnome, or the new jami-qt); and 2. the daemon (dring, or more recently jamid). It’s possible that you killed the client process but the daemon was left running. And since the daemon is the one actually making calls etc then your call would continue.