Kindly explain the stipulation that prohibits the recitation of Naalaayira Divya Prabandham during the months of Margazhi and Tai after Sri Nammazhvar has started from his place of birth:

Two reasons can be ascribed to why Prabandham is not recited at home during the anadhyayana kalam.
At a time in the past, Kaliyan established adhyayana utsavam by ceremoniously bringing Nammazhavar from Azhvartirunagari to Tiruvarangam to recite Azhvar’s Srisuktis in front of Emperuman. This practice is followed to this day. It is an exalted experience to recite Azhvar’s Srisuktis in front of Emperuman during adhyayana utsavam; it appears that to ensure that everyone participates with a single-mindedness to enjoy this experience as a goshti, they might have prohibited the recitation at homes.
In addition to the temples, it seems that elders have conducted adhyayana utsavam at homes where idols were consecrated.
Another reason is, that Divya Prabandham cannot be recited during anadhyayana kalam, it seems this period is an appropriate period to learn and recite the Srisuktis of our Purvacharyas.