What I have typed in the title is all I want to know.
There is no domestic interest rate; there is a world interest rate.
What you presumably mean to ask is: How is that a change in the world interest rate, caused by a change in domestic supply or demand, increases capital inflow?
Answer: Because the foreign supply and demand for output are being held constant, an increase in the interest rate leads foreigners to produce more and consume less. The excess has to go somewhere, i.e. it has to be lent to a non-foreigner, i.e. to a domestic citizen.