As I discuss in this answer, one of the early movements that was important in the development of Vaishnavism was the ancient Pancharatra movement, whose sacred texts consisted of detailed procedures to worship the sage Narayana, an ancient incarnation of Vishnu. Since the Pancharatra texts originated from Narayana himself, they are followed by pretty much all mainstream Vaishnava Sampradayas, whether Sri Vaishnavas, Madhvas, Gaudiya Vaishnavas, etc. In fact you can pretty much define Vaishnavism the belief in the supremacy of Vishnu as it's described in the Pancharatra texts.
But as I discuss in this answer, there is another group of Vishnu-worshippers who worship Vishnu according to a different set of texts, the Vaikhanasas. Vaikhanasas place more emphasis on rituals than in high-minded philosophy; while mainstream Vaishnavas are committed to elaborate Vedantic philosophical systems, like Dvaita or Visistadvaita, Vaikhanasa doctrines are more about the construction and worship of idols and the like. The vast majority of Vishnu-worshippers are Vaishnavas, but there are a few Vaikhanasa temples in India.
In fact, the most popular Vishnu temple in the world, the Tirumala Venkateshwara Temple, is a Vaikhanasa temple. This has led to some tension over its practices, and over whether it should adopt more Pancharatra customs. In [this 2002 article], the Shankaracharya of Kanchi weighed in on this issue:
"There are two kinds of temples. One where the deity comes out on its own or Swayambhu and the other where the deities are installed," he said and added that there are two systems for performing rituals at Vaishnava temples — Pancharatram and Vaikhanasam.
Pancharatra system began during the days of Ramanujacharya, while the other system is traditional. But for the temples where deities are not installed Vaikhanasa is the right system to follow, he explained. There is no place for Pancharatra system there, the swami said.
"Tirumala is one such temple, where the rituals have to be performed according to the traditional Vaikhanasa system," the Shankaracharya said.
So my question is, is the Shankaracharya of Kanchi right that Vishnu temples where the statue is Swayambhu or divinely created are supposed to follow Vaikhanasa rather than Pancharatra?
Here is a list of 8 famous Swayam Vyakta Kshetras, or places where Vishnu manifested as a Swayambhu statue. I think almost all of them have always been run according to Pancharatra. For instance, Sri Rangam is the oldest center of Sri Vaishnavism, and it contains the oldest Swayambhu Vishnu statue as I discuss here. So it seems like either a larger number of Vishnu temples are following the wrong practices, or the Shankaracharya is mistaken.
Does anyone know of any scripture which says that Swayambhu Vishnu statues have to be worshipped according to Vaikhanasa as opposed to Pancharatra?
Here is a list of 8 famous Swayam Vyakta Kshetras?