The information provided by the Shanghai consulate, on the link you give, is somewhat vague as to whether this "permit" is provided in advance or on arrival. It turns out (see below) that you need to apply in advance. I would advise that you contact them (or the appropriate consulate for where you currently live) to clarify the exact procedures required to apply for the visitors' permit at that particular consulate.
The Serbian embassy in Tokyo provides more information:
HOLDERS OF TAIWANESE PASSPORTS
Holders of Taiwanese passports do not need visa to enter Republic of Serbia but prior to travel have to acquire Certificate issued by the Embassy of the Republic of Serbia which certifies that the border authorities of the Republic of Serbia will allow holder of Taiwanese passport to enter Republic of Serbia at the border crossing/airport.
I guess the only difference between a visitors' permit and a visa is that the permit is issued when Serbia does not have diplomatic relations with the country of which the applicant is a citizen.