LEDs lighting up while being baked inside a reflow oven
I'm going to guess that it has to do with the thermocouple I see touching the board vs. the metal insides of the oven (which are touching the bottom of the PCB). 

Insulation conductivity increases exponentially with temperature so a small amount of leakage at room temperature can become quite significant at red heat. 

It probably indicates that your oven interior is not properly earthed.