I do not think it is that simple., cnbc is treating large multi-trillion dollar diversified economies like "Banks issuing CDs"., where an investor chasing a return withdraws from one bank and deposits into another. Overnight.
The rising interest rate impacts everybody, but more so riskier economies. Put it other way around, the risk premium increases. So as a FII if you are planning to invest in Bakistan or Venezuela or Nigeria., now you have to take a pause and look at risk premium and see if it is better to invest more back in US.
However as an FII, you also need to have some exposure to multi-trillion dollar economies (there are very few in the world) - last checked only Eight. And India is expected to climb from current 6th or 7th position to 3rd or 4th position by 2025. So now, do you want to risk your investment in the former to gain for few basis points in later? For some yes, but the quantum of the "outflow" is over exaggerated.
Further the very notion that "rising interest rates in the US" is a fact is to be questioned. In developed economies like US, inflation is generally tied to wage growth. Where is the wage growth in US?
The above note from CNBC/Credit-Suisse would have been valid if it was maybe written in 1918. This is 2018.