I am not sure whether I have stumbled on intended behaviour. I noticed that, when I have a connection tab open and turn the focus to it, it automagically tries to connect (see attached screen cast). To me, this is a bit annoying. I could not find any settings to control this behaviour.
I've opened a ticket that we should look into this.
Just to inform you that we have released DbVisualizer 14.0.1 with a fix for the issue you ran into.
Easiest is that you open Help->Check for Update in DbVisualizer to perform the upgrade. An alternative is that you download from our website: https://www.dbvis.com/download/