This concerns the version in which a light is flashed at the center of a moving train and while the people onboard see the flashes arrive at the two ends simultaneously, the people on the platform see the flash arrive first at the rear end and later at the front end.
Imagine that for the guy onboard the flashes arrive both at noon and the light is so powerful that it burns the hand of the watches that are fixed at the ends of the train exactly at noon position.
What exactly sees the guy on the platform? Obviously he must see the flash burning the hands in the same position, but at different times. This seems to imply that the time flows with different velocities at the two ends of the train w.r.t. the platform, but this cannot true since both of them travel together at the same velocity.
Where am I wrong?