When starting a coop mission with the custom option Tychus’ Joey-Ray’s Bar timer starts when you enter the mutation selection screen, meaning before the mission starts. If you wait long enough in that menu, you can theoretically recruit outlaws before Tychus spawns.
It then causes a 2. bug, which has already been described, you can’t recruit a 5th outlaw, the icons are colored, but when you click on one, it says “not enough charges”