Is it the Anantha Navaneetha Krishnaswamy Temple of Arasalwar? If i remember right Arasalwar is another name for Kulasekara Alwar (not sure though). If true, perhaps your family belonged to Kulasekara Alwar's kulam back in time. (not caste please, its kulam).
Speaking of "kulam", please think of ancient times, when people of one kulam formed one social group. People depended on cattle for their sustenence. So cattle raids were common.
There are ballads eulogizing cattel-raids in Purapporul Venba Malai. The bravest of men was he who could steal or seize many cattle. To be a great stealer of cattle signified great prestige, valor, bravery, in those times.
Kulasekhara Alwar was a Chera chieftain. Chera chieftains, it is said, were nagas. There is some evidence the nagas in some places considered themselves the attendents of Perumal. Hence the association with Sesha Naga perhaps.
Chera chieftains had the title Villavar Kon. Many people claim and associate the title with various present day castes. However villavar can simply mean a great archer. Those were days without swords and metal.
There is also some possibility the Villavars were ancient Bhils, who may have been a 'Bhil kingdom' or a powerful syndicate made up of various/composite tribes in an ancient time, all of whom were clubbed under the nationality/kingdom identity as "Bhils", that is people from "Bhil Kingdom"..
Unfortunately sensibilities of one culture does not make sense to another. So cattle-lifting became associated with 'theft' and got denounced. You can read something about the ancient Bhil Kingdom here
(maybe that is why 'munda' came to be associated with 'robber' in dravidian languages). Here is something on ancient bhil kingdom - http://www.indiatogether.org/photo/2003/bhil.htm
But in the pre-Kuru era of old times, social sensibilties of occupational roles were different. Within a clan or social group, there were various occupations, such as bodyguards of a chieftain, farmers, actors (native theatre), charioteers, garland makers, bards, poets and even people whose duty was to shout periodically the nalikai or time division as it happened (there were no clocks / watches).
Perhaps people realised the instant effect of music and lyrics on the mind. So the priests who sang for their own chieftain, invoked the spirit of god in him, and thus motivated him to win for their own clan, were a very important group (think of people with talent to motivate, those with literary talent, or musically gifted people organising themselves into a club). I suspect these were the beginnings of 'goshti'.
Somewhere along the way clans perished and later caste groups surfaced. Yet people remained associated with their clan deities as kula deivams. IMO a detailed study of kuladeivam koils related across various places, can actually throw some light on the settlement patterns of people.
To me, tracing the orgins of tribes/clans is impossible. We can only imagine that the same people evolved in various cultural phases. It is my personal opinion (without proof though) that present day brahmins of the south are infact native, and have evolved over cultural phases, perhaps deriving their practices from both, native ones as well as adopted ones. An admixture of native priests and incoming vedic brahmins also cannot be discounted per se.
I request you to check the sthala puranam of the temple, to know more about the deity Arasalwar (eg, He belonged to which region, occupation, what was the story due to which the temple was built, etc).
How to worship him? Well, maybe its a nice idea to immerse yourself in his thots, going beyond his persona and sensing the universe through him... automatically along the way perhaps a poem will occur to you. Sing it for him and thus worship him with your love. Maybe some flowers to show love will be a pleasing sight to you and to him. He is the guardian spirit of your kulam afterall, so please him in whatever ways you can and find yourself pleased within, as the spirit in you....