The month of MAHAPARINIBBAN Day of Tathagat Buddha , as per Mahaparinibban Sutta ?

Many people of the Buddhist world celibrate Parinirvana day during first half of the month of February while some people celibrate on Full Moon Day of Vesak month (Indian Months). As I read the Mahaparinibban Sutta, I found Tathagata assures Mara that “Tathagata will have Parinirvan after three months from now.” This time is that, when Tathagata has just finished his Varshavas (Rainy Season) at Veluvgram (near Veshali). It must be the “Assayuja” month (Month just after Rainy Season). According to this, Three months after this will be “Magha” month. (as per Julion Calendar, month of February (first week or so). Why then, some people say that Tathagata got Parinirvana on Vesak Full Moon Day ?