What is confusing? Even if you yourself log out of Twitter, other people are still looking at it. In that sense, they don't cease to exist when you put your phone down, because other people are still paying attention to them.
Sure, as long as they don't know who you are, then it's not such a big deal. An online mob that's mad at you but doesn't know who you are is easy enough to ignore - just log out, as you said. But increasingly it feels like it is less and less likely that the mob does not know who you are. A Twitter mob knows that its outrage is for naught unless it can cause lasting harm to its target, and so it goes to great efforts to dox those targets. Almost always, it seems, the target is doxxed and then their life is ripped to shreds.
Sure, as long as they don't know who you are, then it's not such a big deal. An online mob that's mad at you but doesn't know who you are is easy enough to ignore - just log out, as you said. But increasingly it feels like it is less and less likely that the mob does not know who you are. A Twitter mob knows that its outrage is for naught unless it can cause lasting harm to its target, and so it goes to great efforts to dox those targets. Almost always, it seems, the target is doxxed and then their life is ripped to shreds.