US fed reduced interest rates. Local banks have also reduced interest rates. What's the correlation between US and Sg interest rates, and what are the reasons for the correlation?

Came across many comments saying that the cut in local bank interest rates (DBS multiplier, UOB one.etc) is due to the cut in US interest rate. Just hope to understand the correlation and reasons why. Does it mean that if the US interest rate goes up, Sg/all other countries will follow suit? Why do countries take the lead from US fed's interest rates? Thanks!