Interrelationship between inflation and foreign capital flow
I think the flaw in your reasoning is expecting that foreign capital inflow would lead to more ₹ in circulation.  When investors bring in capital, they are buying ₹ that were previously in circulation.  This additional demand without additional supply is exactly what drives the price of the ₹ up.  There is no increase in the quantity of ₹ circulating unless the government/central bank responds in some way.