Mobilization of units allowed on a territory with an industrial complex controlled by a power on same side?
You may only mobilize units in a territory you (not your ally) have owned since the start of the turn.  Additionally, you liberate allied territories when you capture them, immediately returning ownership to the original owner*. Thus the USSR cannot mobilize in India, since it is owned by the UK, not the USSR.

* - Details, it is technically possible to create a situation where the USSR could mobilize in India. It would require that the Axis captures both the UK capital, and India, then the USSR recapture India (a territory is not liberated if the owner's capital is in enemy hands), then on the following turn (after a full turn of ownership) the USSR may mobilize in India.