Google search for Sri Rama temples in Tamilnadu returns many similar images, with Sita on the right of Rama, as well as many pictures with her being on the left, as usual elsewhere for Lakshmi-Narayana, Sita-Rama, Radha-Krishna etc. Why are South Indian temples so different in this regard?
If the temple is depicting the specific scenario of the deities during marriage then it's correct that the female deity is placed to the right of the male deity.
Because we have from the Atri Smriti:
A woman is [always] the left limb, the husband being alive or dead ; and he the right one. But in a Sraddha, sacrifice, and marriage, a wife should always [be placed] in the right. (138)