Avvai is corruption in tamil of the term avve or avva (both Meaning Mother) in Kannada/Tulu not native to Tamil, indicating origin of legend of Avvaiyar to Karnataka.
Avvai and Muruga (Subramanya) have lot of legendary stories. But we are not able to select a date for these stories. Auvaiyar is shown here as saivite and great devotee of Muruga. Another place Vinayaka (Ganesha) is the god of Avvai and she gets sainthood at the young age by praying to him. Another place Avvai is called a jain. So there is no clear identification here and each sect seems to claim as their own.
The Athichudi is called avvai kural by some. Meaning that Thiruvalluvar and Auvaiyar lived during same period. But today Tamil scholars say that Atticudi was composed by avvaiyar of Kulothunga Period.
Kulothunga III (1178 to 1218AD)
The Traditional accounts of Velir exactly fits Chalukyas, especially Kapilar description of velir. As the new branch of Chalukyas - Chalukya chola came into being, Chalukya and Chola legends mixed and we have lot of confusion. Velirs are from Kuntala that is chalukya country. In kuntala : Kunta means spear same as vel. Thus people of kuntala becomes velir. As we have already seen Velir is Chalukya and Malaya is Hoysala in Sangam Literature in another article.
Adhiyaman sent Auviyar as Ambassador to Thondaiman to prevent war. In Another instance Malayaman kari arch rival of Adigaman meets Avvaiyar and feeds her. This is Sangam Avvaiyar lived during period of Adigaman, Malayaman Kari and Thondaiman. So if we find the dates of these kings, we will find the date of Auvaiyar.
In another inscription in the Kailasanathaswami temple in Kulothunga Chola III mentions thondaiman. Specifies in his twenty-third year the extent of the devaddana lands below the tanks Sirreri and Periyeri at Arumbar, as fixed by Tondaiman Perumalpillai alias Sedirayadevan. Sedirayadevan looks like Sadaiyan who gave patronage to Kamban. Again same period as Avvaiyar.
So Adhiyaman or Adigaman and Thondaiman are of Kulothunga III Period. We already seen that Malaiyaman are Hoysalas. All three kings are present during the period of Kulothunga III. Since the other Avvaiyar lives in Kulothunga III period. Both the Avvaiyars are same.
There is only one Auvaiyar she lived during period of Kulothunga III. The Sangam Age Avvai is a myth.
A Topographical list of the inscriptions of the Madras presidency