The Fed Controls the Fed Funds Rate, Right?

The Fed controls, their main lever is the Fed funds rate. But what they can control is they can control the rate that people lend them money. So if inflation continues to be hot, even if they cut rates, which will make inflation even hotter, that doesn't mean like your consumer mortgage, your just average person's mortgage actually goes down in rates. Like those rates would still stay high if not go up in that situation.