'The Indian Problem' (to give it a name) as I usually see in these threads can be best described as
"The Subcontinental Populations overwhelming the rest of the Imperial populations voting power if given equal franchise"
The details of such a federations parliament would be important, because to prevent 'The Indian Problem' could involve four actions.
1) Not recognising India as a single colony, and ensuring that the Indians don't recognise it either. Have them identify solely as Kannadan, Bengali, Punjabi, Baluch, Sikh, Nepalese, Teluch, etc. With them kept desperate and disparate, it prevents a single common goal being as easily reached.
2) Encouraging white settlers and population growth in the colonies. Given time, a subsidised while settler population encouraged to have white children would increase anglosaxon presences in ALL colonies (If defined as unfederated provinces of the Empire). This would encourage the growth of small white populations in all the african colonies, probably not enough to dominate local politics with equal franchise, but would strengthen them across the empire.
3) Encouraging migration of groups IN and OUT of India. Having Indians in Africa (As OTL) and Britain would reduce any common consensus among Indians as they would have different interests (as would white settlers).
4) Disenfranchise Non-Whites as long as possible. I don't agree with this, but if you start with Whites, then include African and Subcontinental groups as best suits the empire, the problem can be reduced.
Overall, this leads to a redistribution of Subcontinentals and Africans, alongside an increase in Anglo-Saxon populations to achieve something like a (Anglo:Indian:African) 1:1:1 ratio of representation, or more ideally a 2:1:1 - but the latter would be nearly impossible in a few decades without purposeful disenfranchisement.