Evidently the association has many strands and how all of them came together remains unclear. There is the tale of reNukA’s adultery (covered here: TW). 1 persistent narrative is that she obtained the cures of for various poxes and herpes after being banished by j for the adultery from the ashvin-s. She then returned to j with her blemishes cleared with these cures. Now yellamma appears to have been a folk goddess of the poxes. That seems to have been fused with reNukA and mixed with the adultery and beheading tales.
interestingly, the 21 wounds reNukA received in the above-linked tale while attempting to defend jamadagni from the vItahavya-s are said to be the marks of the poxes associated with yellammA
even in the eastern Dravidian country the folk story of the origin of mArI disconnects her from the shaiva tradition and instead has her emerge from reNukA after reNUkA’s head was placed on the body of her servant named chakkalachi. In some Tam mArI temples you will see a figure of a v1 which is none other than jamadagni bhArgava. There are also two other curious figures associated with her. A bull-headed attend called poTTurAja and a v3 hero who also serves as her servant.