The person then simply matches number on article to the number on bin and throws, dead simple.
See my comment above for detailed description of this.
The problem is when items have multiple labels, because they're not made of one thing. The simplest example is Saran wrap, where the box is "paper", and the part to cut plastic is either "aluminium" or "plastic" (there are brands that make it in paper so that it's easier, though). And both parts go in different bins. Bottles can have 3 parts: plastic cap, PET bottle, paper label. All in different bins.
Then you add rules where things need to be clean, which mean in theory, your toothpaste tube needs to be cut open, and cleaned, before putting it in the bin.
And different cities have different rules.
It needs to be dead simple: number of labels = number of bins available. Maybe number of labels can be more than number of bins by 1 or 2 at most.
Secondly, use numbering instead of icons. Numbering is dead simple to match, icons require effort to match on the box against the picture on bin.
In the case of saran wrap: the box should clearly say #2 for box and #3 for contents (saran wrap). That would resolve the case you mentioned.
As for the salan wrap, the point is that it's not a box vs contents problem. The box itself needs to be broken up (removing the cutter part) before being thrown away.