If you go through our history, I find these facts which are mostly unacceptable to many today:
The nAmams did not determine which sampradaya you belonged to - till 18th century. And despite what some tenkalais may claim, both namams have been in use since long before. The oldest representations of namam in stone is seen only from Vijayanagar and in those temples, you find both kinds of namams in the same temple (hazara rama, vijaya vitthala, krishna, anantasayana etc).
Aatthaan jeeyar 1710 agreement gives tenkalais the right to recite their DP taniyan in all the divyadesams in kanchi while Tatacharyas retained the right over Veda and stotra patha in these temples.
In old mysore region, the fight became keen on melkote only from 1710. When the kanchi agreement gave right to tenkalais, similar right was asked in melkote but the 1710 farmaan of maharaja shows that he allowed only vdk taniyan to be recited in melkote as was in practice since Raja wodeyars time (Raja wodeyar ruled in 1576 - hence, the claim that vdk taniyan is only 250 yrs old stands falsified).
But the issue cropped up again in 1780s and in 1784-85, tipu (of all people!!) gave the farmaan to recite both taniyans in melkote temple. Since then, this is the allowed practice in melkote.
The philosophical difference had not led to a great civil war till the 1790s.
The first major rift happened in 1795 when the thelliyasingar sannidhi of Triplicane was taken over by Tenkalais from the Vadakalai side. This lead to a backlash in kanchi where vadakalais wanted to boot out tenkalais from Varadaraja and Thooppul.
Till 1795, Tatacharyas of Kanchi were still ok with the 1710 agreement but post 1795, you see them becoming opposed to the agreement.