In mentioning the details of the sub-sects Tamil Brahmin Iyer Smarthas, particularly Brahacharnams, one more name is left out, i.e. called "Tiruvannaamalai Brahacharnams" to which this writer belongs to. When introducing ourselves to others of this sect or to other sub-sects, they respond reciting "AROHARA" as in praise of the Lord at Tiruvannaamalai. I doubt this is included in one of the other names. Moreover, I had been told by some that Brahacharnams know all the vedas and shastras as their knowledge is 'brihat', i.e. large. Each of these different sub-sects had their own distinct food preferences, eating habits, dressing habits and other idiosyncracies necessitated by geographical or environmental situations. If you ask any Septuagenarian in interior Tamilnaadu they would be able to tell some interesting anectodes on this.Those distinguishing qualities were real and may still be.
How Brahmins (in large numbers) from the North came to the South. I have read a story. When Raja Raja Chola invaded and conquered the North, the vanguished kings offered any thing and every thing to the Victor, the Great Chola had said that he did not want any material gifts (as he had plenty with himself) but wanted to take the priests and vedic scholars as he was impressed by the Poojas and the methods of doing them.
As for migration to other places, there is a story recorded by Dr Smt Sai Sri Rekha, author of 'Meenkulatti Amman Varalaaru' (Pallassna, Palakkad Dt,Kerala))a small booklet on the said temple, done after research. She says there was heavy flooding around Chidambaram which resulted in famine in the area. This could have driven lot of people out of the place who entered into areas which are now in Kerala.