he claims to have used an auto clicker that clicks 60 times per second
18000 / 60 = 300 = 5 minutes
It did last about a minute, but the auto-clicker story is flawed.
When a client is banned it takes the client to the loading screen, then immediately kicks the client to the main menu GUI.
Following that it he'd have to click the "OK" button on the ban reason, "Join a Game", then click the "Join Server" button.
Unless if it was a macro, or some mod adds a rejoin server button. But I doubt that rejoin button would close out the ban reason screen.