While there is some evidence from the early shrIvidyA and siddhAnta tantric sundaranAtha (tirumUlar) was probably from kAshmIra or at least had teachers from kAshmIra, we know little of him and his affiliation with other smArta brAhmaNa-s of the drAviDa country. There a few vaDama-s (Northern smArta-s of the drAviDa country) who believe that they are from kAshmIra. That they were from there is of not much doubt, but whether they form a single migration or came to Tamil Nad (and Andhra) in multiple migrations has not been properly investigated. While eventually we may have the opportunity to investigate these issue with genetic markers, we cannot be so sure given that brahminical tradition is fast eroding in the Tamil country. The smArtas are amongst the most rapidly degenerating communities via varNa sankara, patita sAvitra and other pAtakas.
Looking at inscriptions we find the following information:
1) The oldest layer of vaDamas from the tirunelveli region contain one group of Kashmirian immigrants. This group appears to have come around 750-800 CE and settled specifically in the agrahAra-s associated with the tiruvalishvaram temple. A pallavan incription in this temple clearly attests the settling of these brAhmaNa-s in Tirunelveli. This group was particularly important because they were critical in transmission of the kubjikA tantras and the rahasya-s of the pashchimAnAya. kalhaNa mentions that the confiscation of agrahAras by the king jayApIDa in the dynasty of lalitAditya resulted in many brAhmaNas fleeing and this incident might have been responsible for their southward dispersal.
2) The second layer appears to have been related to the dispersal of an illustrious lineage of Kashmirian brAhmaNa intellectuals who contributed in different realms throughout length of the country. This appears to have happened in the 1000s of CE. This general dispersal included 1) uvaTa, the great vedic commentator who studied vedic grammar and the shukla yajur veda (court of bhoja); 2) bilhaNa the writer and poet who settled in the chAlukya court in karnATaka 3) the father-son-grandson trio: bhAskara (minister), soThala (prime minister) and shAra~Ngadeva (author of the primary sangIta-ratnAkara, the epitome of taurIya gAna) in karNATaka and maharAShTra during the yAdava reign; 4) somashambhu- the illustrious siddhAnta tantric who settled in the Tamil country and wrote one of the primary manuals used in the temple worship of shiva and ritual performance of the mantra-mArga shaivas of the Urdhva-srotas. 5) shrInivAsa bhaTTa- a savant of shrIvidyA who settled in the drAviDa country and initiated several lineages of brAhmaNAs into shrIvidyA. The brAhmaNAs associated with the latter have been incorporated both amongst vaDaMas and shivAchArya in the TN and south-western Andhra.
In between there were the pAshupata kAshmIrAchAryas who settled in the south, but do not appear to have contributed to the gene pool to the best of my knowledge. The final wave appeared during the vijayanagaran rule. This group included several lineages settled during the viceroyship of lakShmaNa daNDanAyaka settled in northern TN. These clans included several vedic experts who served as a priest in sacrifices performed by luminaries like appaya dIkShita. Some these learned the atharva veda in the south and returned to kAshmIra.
Some vaDamas connected to the lATa country might have also originally included a few immigrants from kAshmIra. There is a small community of vaDamas long-settled in Gujarat whose exact connection with these migrations, if any, remains currently unknown to me. It appears that bhAskara-rAya makhIndra’s guru was of this lineage.