How to know when food grade plastic has melted?
Plastic is an amorphous solid. This means that it doesn't have a sharp melting point like water, but it goes through a state where it is softer and softer, until it turns liquid. 

So yes, the plastic was in this state when you touched it. If you want to call this transitional state "melted", then it was melted. Unless you prefer to call it "softened". Everyday language is blurry enough to permit both. 

If you are worried about melted plastic actually mixing throughout the soup, like vinegar would mix if you were to add it, that's not what happened. 

As to "leeching", this is not well defined and not usually covered by food safety rules. Plastics do tend to have overheating restrictions over which they char, but as for "leeching", the only regulated one I know of would be melamine, and I'm pretty sure that's not what your box was made of. So throwing it out or not depends on your personal feelings about leeching.