How did Australia separate from India?
They don't really share a plate, now they did for a long time and the boundary between them is rather recent but they are separate plates.

BUT this was only discovered recently, recently as in 2012, so older references treat them as the same plate.  The "indo" in indo-australian plate is being dropped from more modern references. 



The two plates are moving in almost the exact same direction and speed, so it is easy to see why it took so long to be discovered. Almost is also the key, the forces separating them up is rather weak, tectonically speaking, without a lot of heavy volcanics so the separation is very slow. Now they were not tightly connected to begin with, so there is no continental fault between them. Spreading centers