This topic was discussed in detail by Kamil Zvelebil in his various books. He proves with dating that atleast three different Auvaiyars lived. Some experts have gone to the level of saying 17 Auvaiyars lived. Another common mistake that seemed to have happened is Avaiyar(the spelling starts with first tamil alphabet instead of Auv) means old women. So the poems attributed to the old women got mixed up with Auvaiyar.
Another common phenomena .. I ll start with example 'Kannukul nooru nilava' song music director is some Devendran similarly many songs of Shankar Ganesh, gangai amaran are mistakenly considered as music by Illayaraja(Sun music, illayaraja collections mp3 will have lot of GangaiAmaran, Shankar Ganesh songs).
Similarly when a poet is really famous over a period, all poems written in that period is assumed to be written by the poet. There are so many poems attributed to Kamban but Scholars say the literary patters of Kamba Ramayanam and other dont match at all hence they cant be work of the same author.
With Auvaiyar there are more confusion. Any old women who was poet was most probably confused with Auvaiyar. And again like Agathiyar it was brand name (Agathiyar,Kambar,Auvaiyar are very famous ) so lot of lesser works to get the attention must have been passed as written by Auvaiyar.