If by 'Italians' you refer to native speakers, we don't distinguish among the several 'si', we just use them. :-)
That said, as regards your question the difference between 'si' impersonale and 'si' passivante isn't unanimously agreed upon, and in any case it is a subtle one.
The reasoning behind the classification as "si passivante" is maybe that, while one can certainly consider the 'si' in "In Italia si mangia il tiramisù" very similar to the one in "In Italia si mangia piuttosto bene", the choice of the plural form for 'visti' in "In questa regione non si sono mai visti molti italiani" poses a problem, because, as you probably know, the agreement of the past participle with a postponed direct object is hardly found in the current usage. The problem disappears as soon as one thinks of 'si' as an operator, which, in presence of a "direct object", changes the diathesis of the verb to passive, promoting the direct object itself to the role of subject. Similarly, changing your example "Non si deve usare il cellulare in classe" to "Non si possono utilizzare dispositivi elettronici all'esame", an explanation should be given for the choice of the plural form of the modal verb 'possono', and the same would be necessary for 'usano' in the simpler sentence "Non si usano dispositivi elettronici durante gli esami".
This discussion, while of some relevance in the academy, is clearly of little value to students who simply want to speak and understand the language: the only thing they need to know is that, in presence of a direct object/subject, the verb agrees in both number and gender with it.