The subject of this article originates from non-canonical sources. To find out about what is considered "canon" see LOTR:Canon.
Neither Sebastian nor any of the incidents involving Radagast in the movie were ever mentioned in any of Tolkien's writings; they are a complete Peter Jackson invention for the movie. In Tolkien's writings the forest had become darker, thicker, and infested with spiders, bats, and orcs after the Necromancer (Sauron) occupied Dol Guldur in the southern part of the forest, but there was no mention of any magic that started poisoning all the animals.
Sebastian may also be a subtle reference to Tolkien as a medievalist and/or a Catholic author. In the medieval legend of St. Sebastian, the saint was tied to a post and shot with many arrows. The writer of the legend notes that Sebastian "was pierced with as many shafts as a hedgehog has spines", but he miraculously survived the attempted execution, only to be martyred later by being cudgeled to death. In his Lives of Saints, the Anglo-Saxon homilist Aelfric recounts the legend of Sebastian, and there is also a more widely-known Latin version of Sebastian's story in The Golden Legend; as someone probably familiar with these texts, Tolkien would have appreciated this in-joke. However, this reading of Sebastian's name rests on the assumption that Peter Jackson or one of the film's other writers would have had some contact with an original or translated version of the legend.