The Rahasyatraya Sara is a work by the Sri Vaishnava Acharya Vedanta Desikan, concerning the meaning of the Rahasya Traya or three secrets of the Sri Vaishnava sect (of which I am a member). (One of these secrets is the Dvaya mantra used to surrender to Vishnu, which I discuss here.) In this excerpt from the Rahasyatraya Sara, Vedanta Desikan discusses the philosophy of Visishtadvaita, according to which Jivatmas (individual souls) and matter are part of Vishnu:
Just as Iswara [Vishnu] is the abode, ashraya or adhara (support) of the attributes which define His essential nature (svarupa viz. Satyam, Jnanam, Anandam, and the like) and of the other qualities possessed by Him with his essential nature so defined (qualities like compassion and accessibility), He is also the inseparable and direct support (ashraya or adhara) of all substances (sentient or non-sentient) other than Himself. He is also the support, through these substances ((i.e.) indirectly), of the qualities that pertain to them. There are some who hold that Iswara is the support, through the jivas, of the bodies supported by the jivas. Some Acharyas say (on the other hand) that both directly by His essential nature and indirectly through the jivas, He is the support of these bodies.
So everyone agrees that the Jivatma or individual soul sustains the body, because the body can't live without the soul. But the question is how Vishnu sustains the body. It seems that some believe that Vishnu only sustains the body indirectly, through the Jivatma. Others believe that in addition to sustaining the body through the Jivatma, Vishnu also sustains the body directly.
My question is, which of these two views does the Sri Vaishnava sect subscribe to? Is this something that different Sri Vaishnava Acharyas disagree about? Is this a difference between Thenkalais and Vadakalais, the two main sub-sects of the Sri Vaishnava sect?