This sort of thing has long been a labor issue. At the mine, we were paid “from collar to collar”, that was from the time the cage (think elevator) left the surface until when it returned to the surface. The union persistently bargained for pay from the time you entered the change room to dress for work until after you showered and put on your civilian clothes. The union never got their way either by bargaining or by wage and hour complaints.
That's a somewhat different issue. Unless the work clothes are company property (which isn't indicated by the description), the workers could choose to just go home without changing or showering. The Amazon workers in the present case do not have any such choice, and in the view of rational people (as opposed to the clowns on the bench) are clearly "on the clock".