When the Federal Reserve cuts interest rates, short-term loans like car loans, credit cards, and home equity loans automatically get cheaper because they are based on the Prime rate. Long-term loans like mortgages aren't because they're based on investments that compete with each other, like buying stocks instead of real estate.
When the Fed cuts interest rates, the stock market sees it as a sign that everything is fine. This makes stocks a better investment. This causes money to leave the mortgage-backed securities and bond markets and go into the stock market. This lowers the demand for mortgage-backed securities and bonds.
Now, companies that sell bonds and mortgage-backed securities raise the rates to bring investors back with higher yields, which are the same thing as higher rates. Since the yields are going up, the mortgage rates must also go up.
If the yields or rates on mortgage-backed securities go up, the rates on the mortgages they are backed by must also go up. So, when the Fed cuts interest rates, mortgage rates can go up.